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cleartomark
%%EndFont
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.0)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMCSC10)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
0
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/CMCSC10
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
14
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}
readonly
def
/UniqueID
5000772
def
currentdict
end
currentfile
eexec
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cleartomark
%%EndFont
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.0)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMR7)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
0
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/CMR7
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
-27
-250
1122
750
}
readonly
def
/UniqueID
5000790
def
currentdict
end
currentfile
eexec
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cleartomark
%%EndFont
%%BeginFont: CMTI8
%!PS-AdobeFont-1.1: CMTI8 1.0
%%CreationDate: 1991 Aug 18 21:07:42
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.0)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMTI8)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
-14.04
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/CMTI8
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
-35
-250
1190
750
}
readonly
def
/UniqueID
5000826
def
currentdict
end
currentfile
eexec
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cleartomark
%%EndFont
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(2.1)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(MSBM10)
readonly
def
/FamilyName
(Euler)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
0
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/MSBM10
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
82
/R
put
readonly
def
/FontBBox
{
-55
-420
2343
920
}
readonly
def
/UniqueID
5031982
def
currentdict
end
currentfile
eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
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364A65B9F1F9C6416198FB016FC8456DEEFED46BF4E1F873527AF52C13078ABF
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cleartomark
%%EndFont
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.0)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMSY7)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
-14.035
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/CMSY7
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
-15
-951
1252
782
}
readonly
def
/UniqueID
5000817
def
currentdict
end
currentfile
eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
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A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85
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221A37D9A807DD01161779DDE7D251491EBF65A98C9FE2B1CF8D725A70281949
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1B13FC4967F4CC16F5D3FB5352C593E7CD5E3508EFECE5D27686A78EECC955F3
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2D54A0CD326959B23FC19969761DC350E6B1058261C04C4BC2D7B140A42C336C
20201212D8C2F52ED7B96C1C4C796AE1EBA3939981919A3312A9C415CD7EF42C
BB28EBA3489F813AA123F560B565311771BDDBB356202F5B0A87B02AFFB61EE7
EA3B8E2D2DE8B47F72F8C982C041D4D1141DB48D6ED77FC1CA7937B618308358
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120A0CC8FC87BD1FA7B4776D02EA957DB6F5621B3E41F04550D09C81E6454A47
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0000000000000000000000000000000000000000000000000000000000000000
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cleartomark
%%EndFont
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.0)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMSY10)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
-14.035
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/CMSY10
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
-29
-960
1116
775
}
readonly
def
/UniqueID
5000820
def
currentdict
end
currentfile
eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4
A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85
E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A
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27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF
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0FCE8DD1301C03FBD890F1C26F64E54463FCC31D887EAD4E86CFB5375028072B
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0000000000000000000000000000000000000000000000000000000000000000
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cleartomark
%%EndFont
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.100)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMMI7)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
-14.04
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/CMMI7
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
0
-250
1171
750
}
readonly
def
/UniqueID
5087382
def
currentdict
end
currentfile
eexec
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532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470
B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B
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D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F
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B078D20B4B8A6D7F0300CF694E6956FF9C29C84FCC5C9E8890AA56B1BC60E868
DA8488AC4435E6B5CE34EA88E904D5C978514D7E476BF8971D419363125D4811
4D886EDDDCDDA8A6B0FDA5CF0603EA9FA5D4393BEBB26E1AB11C2D74FFA6FEE3
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012318EA7AA39900C97B9D3859E3D0B04750B8390BF1F1BC29DC22BCAD50ECC6
A3C633D0937A59E859E5185AF9F56704708D5F1C50F78F43DFAC43C4E7DC9413
44CEFE43279AFD3C167C942889A352F2FF806C2FF8B3EB4908D50778AA58CFFC
4D1B14597A06A994ED8414BBE8B26E74D49F6CF54176B7297CDA112A69518050
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cleartomark
%%EndFont
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.100)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMMI10)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
-14.04
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/CMMI10
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
-32
-250
1048
750
}
readonly
def
/UniqueID
5087385
def
currentdict
end
currentfile
eexec
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cleartomark
%%EndFont
%%BeginFont: CMTT10
%!PS-AdobeFont-1.1: CMTT10 1.00B
%%CreationDate: 1992 Apr 26 10:42:42
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.00B)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMTT10)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
0
def
/isFixedPitch
true
def
end
readonly
def
/FontName
/CMTT10
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
-4
-235
731
800
}
readonly
def
/UniqueID
5000832
def
currentdict
end
currentfile
eexec
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cleartomark
%%EndFont
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.00B)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMR10)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
0
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/CMR10
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
-251
-250
1009
969
}
readonly
def
/UniqueID
5000793
def
currentdict
end
currentfile
eexec
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cleartomark
%%EndFont
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.0)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMR8)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Medium)
readonly
def
/ItalicAngle
0
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/CMR8
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
-36
-250
1070
750
}
readonly
def
/UniqueID
5000791
def
currentdict
end
currentfile
eexec
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cleartomark
%%EndFont
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11
dict
begin
/FontInfo
7
dict
dup
begin
/version
(1.00B)
readonly
def
/Notice
(Copyright (C) 1997 American Mathematical Society. All Rights Reserved)
readonly
def
/FullName
(CMBX10)
readonly
def
/FamilyName
(Computer Modern)
readonly
def
/Weight
(Bold)
readonly
def
/ItalicAngle
0
def
/isFixedPitch
false
def
end
readonly
def
/FontName
/CMBX10
def
/PaintType
0
def
/FontType
1
def
/FontMatrix
[
0.001
0
0
0.001
0
0
]
readonly
def
/Encoding
256
array
0
1
255
{
1
index
exch
/.notdef
put
}
for
dup
0
/.notdef
put
readonly
def
/FontBBox
{
-301
-250
1164
946
}
readonly
def
/UniqueID
5000768
def
currentdict
end
currentfile
eexec
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begin
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0
bop
893
716
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2462
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(dual)
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(cone.)
456
3336
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Fj
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f
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(implies)
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(ariables)
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(e.)
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32
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(tain)
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(the)
456
3435
y
(problem)
d
(data,)
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(if)
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(either)
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(b)
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Fl
(or)
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Fl
(is)
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(then)
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(is)
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(treated)
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(as)
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(zero.)
555
3535
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(The)
33
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(structure)
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(K)
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(de
\014
nes)
32
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(the)
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(cone)
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(w)
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(y:)
45
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(it)
32
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(can)
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(ha)
n
(v)
n
(e)
f
(
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elds)
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Fj
(K.f)
p
Fl
(,)
456
3635
y
Fj
(K.l)
p
Fl
(,)
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Fj
(K.q)
p
Fl
(,)
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Fj
(K.r)
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Fl
(and)
i
Fj
(K.s)
p
Fl
(,)
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(for)
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(F)
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b
(ree,)
31
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(Linear,)
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(Rotated)
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(quadratic)
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(and)
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(Semi-)
456
3734
y
(de
\014
nite.)
36
b
(In)
24
b
(addition,)
h
(there)
f
(are)
f
(
\014
elds)
h
Fj
(K.xcomplex)
p
Fl
(,)
d
Fj
(K.scomplex)
f
Fl
(and)
k
Fj
(K.ycomplex)
c
Fl
(for)
456
3834
y
(complex-v)
-5
b
(ariables.)
597
3953
y
(
\(
1
\)
)
41
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Fj
(K.f)
33
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Fl
(is)
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(the)
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(n)
n
(um)
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(b)
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(er)
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(of)
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(FREE,)
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(i.e.,)
j
(UNRESTRICTED)
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(primal)
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(comp)
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(onen)
n
(ts.)
744
4053
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(The)
20
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(dual)
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(comp)
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(onen)
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(ts)
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(are)
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(to)
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(b)
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(zero.)
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(E.g.)
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(if)
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Fj
(K.f)
42
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(=)
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(2)
20
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Fl
(then)
g
Fj
(x
\(
1:2
\)
)
744
4152
y
Fl
(is)
k
(unrestricted,)
h
(and)
f
Fj
(s
\(
1:2
\)
=0)
p
Fl
(.)
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(These)
24
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(are)
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(AL)
-9
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(W)
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(A)
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(YS)
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(the)
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(
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rst)
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(comp)
r
(onen)
n
(ts)
g
(in)
744
4252
y
Fj
(x)
p
Fl
(.)
597
4351
y
(
\(
2
\)
)
41
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Fj
(K.l)
27
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Fl
(is)
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(the)
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(n)
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(um)
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(b)
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(er)
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(of)
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(NONNEGA)
-7
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(TIVE)
28
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(comp)
r
(onen)
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(ts.)
38
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(E.g.,)
28
b
(if)
g
Fj
(K.f=2)
p
Fl
(,)
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Fj
(K.l=8)
744
4451
y
Fl
(then)
i
Fj
(x
\(
3:10
\)
>=0)
p
Fl
(.)
597
4551
y
(
\(
3
\)
)
41
b
Fj
(K.q)
106
b
Fl
(lists)
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(the)
f
(dimensions)
g
(of)
h
(LORENTZ)
e
(
\(
quadratic,)
126
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(second-)
744
4650
y
(order)
67
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(cone
\)
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(constrain)
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(ts.)
157
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78
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(if)
69
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Fj
(K.l=10)
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Fj
(K.q)
43
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(=)
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([3)
g
(7])
67
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Fl
(then)
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4750
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Fj
(x
\(
11
\)
)
42
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(>=)
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(norm
\(
x
\(
12:13
\)\)
)
p
Fl
(,)
72
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Fj
(x
\(
14
\)
>=)
41
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(norm
\(
x
\(
15:20
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)
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Fl
(.)
152
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(These)
68
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(com-)
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4850
y
(p)
r
(onen)
n
(ts)
55
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(AL)
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(A)
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(immediately)
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(follo)
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(w)
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(the)
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Fj
(K.l)
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Fl
(nonnegativ)
n
(e)
h
(ones.)
117
b
(If)
744
4949
y
(the)
48
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(en)
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(tries)
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(in)
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Fi
(A)
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Fl
(and/or)
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Fi
(c)
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Fl
(are)
f
(COMPLEX,)
g
(then)
h
(the)
h
Fi
(x)
p
Fl
(-comp)
r
(onen)
n
(ts)
e
(in)
p
456
5039
499
4
v
555
5133
a
Fd
(Date)
5
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Fm
(:)
23
b
(June)
i
(16,)
e
(2005.)
555
5216
y
(Based)
h
(on)
g
(the)
h
(original)
e
(SeDuMi)
g
(User)
g
(Guide)
i
(and)
f
(the)
g
(con)
n
(ten)
n
(ts)
i
(of)
d
(the)
i
(SeDuMi)
e
(help.)
1933
5315
y
Fc
(1)
p
eop
end
%%Page: 2 2
TeXDict
begin
2
1
bop
456
251
a
Fc
(2)
1256
b
(IMRE)
22
b
(P)
1998
236
y
(
\023
)
1989
251
y
(OLIK)
744
450
y
Fj
(norm
\(
x
\(
#,#
\)\)
)
46
b
Fl
(tak)
n
(e)
k
(complex-v)
-5
b
(alues,)
56
b
(whenev)
n
(er)
50
b
(that)
h
(is)
g
(b)
r
(ene
\014
cial.)
106
b
(Use)
744
550
y
Fj
(K.ycomplex)
24
b
Fl
(to)
j
(imp)
r
(ose)
h
(constrain)
n
(ts)
e
(on)
h
(the)
h
(imaginary)
e
(part)
h
(of)
h
Fj
(A*x)
p
Fl
(.)
597
649
y
(
\(
4
\)
)
41
b
Fj
(K.r)
20
b
Fl
(lists)
i
(the)
f
(dimensions)
g
(of)
g
(Rotated)
h
(LORENTZ)
e
(constrain)
n
(ts.)
33
b
(E.g.,)
22
b
(if)
g
Fj
(K.l=10)
p
Fl
(,)
744
749
y
Fj
(K.q=[3,7])
j
Fl
(and)
k
Fj
(K.r)
42
b
(=)
h
([4)
g
(6])
p
Fl
(,)
28
b
(then)
i
Fj
(2*x
\(
21
\)
x
\(
22
\)
)
38
b
(>=)
43
b
(norm
\(
x
\(
23:24
\)\)
^2)
744
849
y
Fl
(and)
23
b
Fj
(2*x
\(
25
\)
x
\(
26
\)
>=nor)
o
(m
\(
x)
o
(
\(
2)
o
(7:3)
o
(0
\)
)
o
(
\)
^)
o
(2)
p
Fl
(.)
30
b
(These)
23
b
(comp)
r
(onen)
n
(ts)
f
(AL)
-9
b
(W)
g
(A)
i
(YS)
24
b
(im-)
744
948
y
(mediately)
30
b
(follo)
n
(w)
e
(the)
i
Fj
(K.q)
e
Fl
(ones.)
41
b
(Just)
29
b
(as)
g
(for)
g
(the)
g
Fj
(K.q)
p
Fl
(-v)
-5
b
(ariables,)
27
b
(the)
j
(v)
-5
b
(ariables)
744
1048
y
(in)
30
b
Fj
(norm
\(
x
\(
#,#
\)\)
)
24
b
Fl
(are)
k
(allo)
n
(w)
n
(ed)
g
(to)
h
(b)
r
(e)
h
(complex,)
f
(if)
h
(y)
n
(ou)
e
(pro)
n
(vide)
g
(complex)
h
(data.)
744
1147
y
(Use)
f
Fj
(K.ycomplex)
23
b
Fl
(to)
28
b
(imp)
r
(ose)
f
(constrain)
n
(ts)
g
(on)
g
(the)
h
(imaginary)
e
(part)
h
(of)
h
Fj
(A*x)
p
Fl
(.)
597
1247
y
(
\(
5
\)
)
41
b
Fj
(K.s)
79
b
Fl
(lists)
h
(the)
g
(dimensions)
g
(of)
g
(POSITIVE)
f
(SEMI-DEFINITE)
g
(
\(
PSD
\)
)
744
1347
y
(constrain)
n
(ts.)
208
b
(If)
86
b
Fj
(K.l=10)
p
Fl
(,)
97
b
Fj
(K.q)
43
b
(=)
g
([3)
f
(7])
85
b
Fl
(and)
g
Fj
(K.s)
42
b
(=)
h
([4)
g
(3])
p
Fl
(,)
99
b
(then)
744
1446
y
Fj
(mat
\(
)
42
b
(x
\(
21:36
\)
,4)
e
(
\)
)
35
b
Fl
(is)
h
(PSD,)
g
Fj
(mat
\(
)
41
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(x
\(
37:45
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(
\)
)
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Fl
(is)
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(PSD.)
g
(These)
f
(comp)
r
(o-)
744
1546
y
(nen)
n
(ts)
28
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(are)
e
(AL)
-9
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(W)
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(A)
i
(YS)
29
b
(the)
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(last)
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(en)
n
(tries)
g
(in)
h
(x.)
837
1646
y
Fg
(
\017
)
41
b
Fj
(K.xcomplex)
26
b
Fl
(lists)
31
b
(the)
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(comp)
r
(onen)
n
(ts)
g
(in)
g
(f,l,q,r)
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(blo)
r
(c)
n
(ks)
g
(that)
h
(are)
f
(allo)
n
(w)
n
(ed)
g
(to)
920
1745
y
(ha)
n
(v)
n
(e)
c
(nonzero)
g
(imaginary)
g
(part)
h
(in)
h
(the)
g
(primal.)
837
1845
y
Fg
(
\017
)
41
b
Fj
(K.scomplex)
24
b
Fl
(lists)
29
b
(the)
g
(PSD)
g
(blo)
r
(c)
n
(ks)
f
(that)
h
(are)
e
(Hermitian)
i
(rather)
f
(than)
g
(real)
920
1944
y
(symmetric.)
837
2044
y
Fg
(
\017
)
41
b
Fl
(Use)
27
b
Fj
(K.ycomplex)
d
Fl
(to)
j
(imp)
r
(ose)
h
(constrain)
n
(ts)
e
(on)
h
(the)
h
(imaginary)
e
(part)
h
(of)
h
Fj
(A*x)
p
Fl
(.)
555
2174
y
(The)
f
(dual)
f
(m)
n
(ultipliers)
h
Fi
(y)
i
Fl
(ha)
n
(v)
n
(e)
d
(analogous)
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(meaning)
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(as)
g
(in)
h
(the)
g
Fj
(x>=0)
e
Fl
(case,)
h
(except)
g
(that)
456
2274
y
(instead)
33
b
(of)
g
Fj
(c-A'*y>=0)
c
Fl
(resp.)
53
b
Fj
(-A'*y>=0)
p
Fl
(,)
31
b
(one)
i
(should)
g
(read)
f
(that)
i
Fj
(c-A'*y)
d
Fl
(resp.)
52
b
Fj
(-A'*y)
456
2374
y
Fl
(are)
37
b
(in)
h
(the)
g
(cone)
g
(that)
g
(is)
g
(describ)
r
(ed)
g
(b)
n
(y)
g
Fj
(K.l)
p
Fl
(,)
i
Fj
(K.q)
c
Fl
(and)
i
Fj
(K.s)
p
Fl
(.)
67
b
(In)
39
b
(the)
f
(ab)
r
(o)
n
(v)
n
(e)
f
(example,)
456
2473
y
(if)
f
Fj
(z)
43
b
(=)
h
(c-A'*y)
33
b
Fl
(and)
j
Fj
(mat
\(
z
\(
21:36
\)
,4
\)
)
30
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Fl
(is)
37
b
(not)
f
(symmetric/Hermitian,)
h
(then)
g
(p)
r
(ositiv)
n
(e)
456
2573
y
(semi-de
\014
niteness)
27
b
(re
\015
ects)
g
(the)
h
(symmetric/Hermitian)
f
(parts,)
g
(i.e.)
37
b
Fj
(s)
43
b
(+)
g
(s')
27
b
Fl
(is)
g
(PSD.)
555
2673
y
(If)
c
(the)
f
(mo)
r
(del)
g
(con)
n
(tains)
g
(COMPLEX)
f
(data,)
h
(then)
h
(y)
n
(ou)
e
(ma)
n
(y)
h
(pro)
n
(vide)
e
(a)
i
(list)
g
Fj
(K.ycomplex)
p
Fl
(,)
456
2772
y
(with)
28
b
(the)
g
(follo)
n
(wing)
e
(meaning:)
661
2902
y
Fg
(
\017
)
41
b
Fj
(y
\(
i
\)
)
26
b
Fl
(is)
i
(complex)
f
(if)
h
Fj
(ismember
\(
i,K.yco)
o
(mpl)
o
(ex)
o
(
\)
)
661
3002
y
Fg
(
\017
)
41
b
Fj
(y
\(
i
\)
)
26
b
Fl
(is)
i
(real)
f
(otherwise)
456
3132
y
(The)
g
(equalit)
n
(y)
g
(constrain)
n
(ts)
f
(in)
i
(the)
g
(primal)
f
(are)
g
(then)
h
(as)
f
(follo)
n
(ws:)
661
3263
y
Fg
(
\017
)
41
b
Fj
(A
\(
i,:
\)
*x)
g
(=)
i
(b
\(
i
\)
)
26
b
Fl
(if)
i
Fj
(imag
\(
b
\(
i
\)\)
)
39
b
(~=)
k
(0)
27
b
Fl
(or)
g
Fj
(ismember
\(
i,K.yco)
o
(mpl)
o
(ex)
o
(
\)
)
661
3362
y
Fg
(
\017
)
41
b
Fj
(real
\(
A
\(
i,:
\)
*x
\)
)
d
(=)
43
b
(b
\(
i
\)
)
26
b
Fl
(otherwise.)
456
3492
y
(Th)
n
(us,)
e
(equalit)
n
(y)
g
(constrain)
n
(ts)
f
(on)
h
(b)
r
(oth)
h
(the)
g
(real)
e
(and)
i
(imaginary)
d
(part)
i
(of)
h
Fj
(A
\(
i,:
\)
*x)
c
Fl
(should)
456
3592
y
(b)
r
(e)
28
b
(listed)
f
(in)
h
(the)
g
(
\014
eld)
g
Fj
(K.ycomplex)
p
Fl
(.)
555
3692
y
(Y)
-7
b
(ou)
31
b
(ma)
n
(y)
f
(use)
h
Fj
(EIGK
\(
x,K
\)
)
c
Fl
(and)
j
Fj
(EIGK
\(
c-A'*y,K
\)
)
c
Fl
(to)
k
(c)
n
(hec)
n
(k)
g
(that)
h
Fj
(x)
g
Fl
(and)
f
Fj
(c-A'*y)
e
Fl
(are)
456
3791
y
(in)
f
(the)
h
(cone)
g
Fj
(K)
p
Fl
(.)
1731
4036
y
(3.)
41
b
Fk
(Options)
555
4186
y
Fl
(Most)
21
b
(of)
h
(the)
f
(options)
g
(in)
g
(SeDuMi)
i
(can)
e
(b)
r
(e)
g
(o)
n
(v)
n
(erridden)
f
(b)
n
(y)
h
(sp)
r
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g
(them)
h
(explicitly)
f
(in)
456
4285
y
(the)
29
b
(structure)
f
Fj
(pars)
p
Fl
(.)
40
b
(This)
29
b
(structure)
f
(can)
h
(ha)
n
(v)
n
(e)
e
(the)
j
(follo)
n
(wing)
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(
\014
elds)
h
(
\(
the)
g
(default)
h
(v)
-5
b
(alue)
456
4385
y
(is)
27
b
(in)
h
(brac)
n
(k)
n
(ets
\)
.)
456
4587
y
(3.1.)
40
b
Fn
(General)
32
b
(options.)
645
4717
y
(pars.
\014
d)
g
(
\(
1
\)
:)
41
b
Fl
(The)
32
b
(output)
g
(of)
g
(SeDuMi)
h
(is)
f
(written)
g
(to)
g
(the)
h
(
\014
le)
f
(with)
h
(handle)
f
Fj
(fid)
p
Fl
(.)
744
4817
y
(If)
k
Fj
(fid=0)
p
Fl
(,)
e
(then)
i
(SeDuMi)
g
(runs)
e
(quietly)
-7
b
(,)
37
b
(i.e.,)
g
(there)
e
(is)
f
(no)
h
(screen)
f
(output.)
59
b
(Use)
744
4917
y
Fj
(fopen)
26
b
Fl
(to)
h
(assign)
g
(a)
g
(handle)
g
(to)
h
(a)
f
(
\014
le.)
645
5016
y
Fn
(pars.maxiter)
32
b
(
\(
150
\)
:)
40
b
Fl
(The)
g
(maxim)
n
(um)
g
(n)
n
(um)
n
(b)
r
(er)
g
(of)
g
(iterations.)
73
b
(In)
40
b
(most)
g
(cases)
744
5116
y
(SeDuMi)
24
b
(stops)
f
(after)
g
(20-30)
e
(iterations,)
j
(and)
f
(almost)
f
(nev)
n
(er)
h
(needs)
g
(more)
f
(than)
i
(100)
744
5216
y
(iterations.)
p
eop
end
%%Page: 3 3
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begin
3
2
bop
1472
251
a
Fc
(SEDUMI)
28
b
(REFERENCE)
h
(GUIDE)
983
b
(3)
645
450
y
Fn
(pars.eps)
31
b
(
\(
)
p
Fl
(10)
1135
420
y
Ff
(
\000
)
p
Fc
(8)
1223
450
y
Fn
(
\)
:)
41
b
Fl
(Desired)
59
b
(accuracy)
-7
b
(.)
128
b
(If)
59
b
(this)
g
(accuracy)
e
(is)
i
(ac)
n
(hiev)
n
(ed)
e
(then)
744
550
y
Fj
(info.numerr)
36
b
Fl
(is)
41
b
(set)
f
(to)
h
(0.)
75
b
(If)
41
b
Fj
(pars.eps=0)
36
b
Fl
(then)
41
b
(SeDuMi)
g
(runs)
g
(as)
e
(long)
h
(as)
744
649
y
(it)
28
b
(can)
g
(mak)
n
(e)
e
(progress.)
645
749
y
Fn
(pars.bigeps)
k
(
\(
)
p
Fl
(10)
1262
719
y
Ff
(
\000
)
p
Fc
(3)
1351
749
y
Fn
(
\)
:)
41
b
Fl
(In)
57
b
(case)
f
(the)
i
(desired)
e
(accuracy)
g
Fj
(pars.eps)
d
Fl
(cannot)
k
(b)
r
(e)
744
849
y
(ac)
n
(hiev)
n
(ed,)
48
b
(the)
d
(solution)
f
(is)
g
(tagged)
f
(as)
h
Fj
(info.numerr=1)
39
b
Fl
(if)
45
b
(it)
g
(is)
f
(accurate)
g
(to)
744
948
y
Fj
(pars.bigeps)
p
Fl
(,)
24
b
(otherwise)
i
(it)
i
(yields)
g
Fj
(info.numerr=2)
p
Fl
(.)
645
1048
y
Fn
(pars.alg)
j
(
\(
2
\)
:)
41
b
Fl
(If)
48
b
Fj
(pars.alg=0)
p
Fl
(,)
g
(then)
f
(a)
g
(
\014
rst-order)
e
(wide)
i
(region)
f
(algorithm)
g
(is)
744
1147
y
(used,)
31
b
(not)
f
(recommended.)
43
b
(If)
30
b
Fj
(pars.alg=1)
p
Fl
(,)
d
(then)
j
(SeDuMi)
h
(uses)
e
(the)
i
(cen)
n
(tering-)
744
1247
y
(predictor-corrector)
19
b
(algorithm)
j
(with)
h
(v-linearization.)
34
b
(If)
23
b
Fj
(pars.alg=2)
p
Fl
(,)
d
(then)
j
Fi
(xz)
t
Fl
(-)
744
1347
y
(linearization)
i
(is)
h
(used)
g
(in)
h
(the)
f
(corrector,)
e
(similar)
i
(to)
g
(Mehrotra's)
e
(algorithm.)
35
b
(The)
744
1446
y
(wide-region)
24
b
(cen)
n
(tering)
g
(predictor-corrector)
d
(algorithm)
j
(w)
n
(as)
h
(prop)
r
(osed)
f
(in)
h
(Chap-)
744
1546
y
(ter)
j
(7)
f
(of)
g
([2].)
645
1646
y
Fn
(pars.theta)
32
b
(
\(
0.25
\)
,)
e
(pars.b)
s
(eta)
i
(
\(
0.5
\)
:)
40
b
Fl
(These)
30
b
(are)
f
(the)
i
(wide)
f
(region)
f
(and)
h
(neigh-)
744
1745
y
(b)
r
(orho)
r
(o)
r
(d)
40
b
(parameters.)
72
b
(V)
-7
b
(alid)
40
b
(c)
n
(hoices)
f
(are)
g
(0)
k
Fi
(<)
g
Fj
(pars.theta)
d
Fg
(
\024
)
j
Fl
(1)
d
(and)
g
(0)
j
Fi
(<)
744
1845
y
Fj
(pars.beta)
20
b
Fi
(<)
i
Fl
(1.)
36
b
(Setting)
25
b
Fj
(pars.theta=1)
19
b
Fl
(w)
n
(ould)
24
b
(restrict)
g
(the)
h
(iterates)
f
(to)
g
(follo)
n
(w)
744
1944
y
(the)
30
b
(cen)
n
(tral)
f
(path)
h
(in)
g
(an)
f
Fi
(N)
1645
1956
y
Fc
(2)
1682
1944
y
Fl
(
\(
)
p
Fi
(
\014
)
t
Fl
(
\)
-neigh)
n
(b)
r
(ourho)
r
(o)
r
(d.)
43
b
(In)
30
b
(practice,)
g
(SeDuMi)
g
(rounds)
744
2044
y
Fj
(pars.beta)
25
b
Fl
(to)
j
(b)
r
(e)
h
(b)
r
(et)
n
(w)
n
(een)
f
(0)
p
Fi
(:)
p
Fl
(1)
g
(and)
g
(0)
p
Fi
(:)
p
Fl
(9)
f
(and)
h
Fj
(pars.theta)
d
Fl
(to)
j
(b)
r
(e)
h
(b)
r
(et)
n
(w)
n
(een)
f
(0)
p
Fi
(:)
p
Fl
(01)
744
2144
y
(and)
g
(1.)
645
2243
y
Fn
(pars.step)
s
(dif)
i
(
\(
2
\)
:)
41
b
Fl
(If)
32
b
Fj
(pars.stepdif=0)
26
b
Fl
(then)
32
b
(the)
g
(primal-dual)
f
(step)
g
(di
\013
eren)
n
(tia-)
744
2343
y
(tion)
26
b
(is)
g
(alw)
n
(a)
n
(ys)
e
(disabled,)
i
(while)
g
(if)
h
Fj
(pars.stepdif=1)
20
b
Fl
(then)
26
b
(it)
h
(is)
f
(alw)
n
(a)
n
(ys)
e
(enabled.)
744
2443
y
(Using)
31
b
(step)
g
(di
\013
eren)
n
(tiation)
g
(helps)
g
(if)
g
(the)
g
(problem)
g
(is)
f
(ill-conditioned)
h
(or)
f
(the)
h
(al-)
744
2542
y
(gorithm)
26
b
(is)
f
(close)
h
(to)
g
(con)
n
(v)
n
(ergence.)
33
b
(Setting)
27
b
Fj
(pars.stepdif=2)
20
b
Fl
(uses)
26
b
(an)
f
(adaptiv)
n
(e)
744
2642
y
(sc)
n
(heme:)
37
b
(it)
28
b
(starts)
f
(SeDuMi)
h
(with)
g
(step-di
\013
eren)
n
(tiation)
f
(disabled)
g
(and)
h
(enables)
f
(it)
837
2742
y
Fg
(
\017
)
41
b
Fl
(after)
27
b
(20)
g
(iterations,)
f
(or)
837
2841
y
Fg
(
\017
)
41
b
Fl
(if)
28
b
Fj
(feasratio)
c
Fl
(is)
j
(b)
r
(et)
n
(w)
n
(een)
h
(0.9)
e
(and)
i
(1.1,)
f
(or)
837
2941
y
Fg
(
\017
)
41
b
Fl
(more)
26
b
(than)
i
(one)
f
(conjugate)
g
(gradien)
n
(t)
g
(iterate)
g
(is)
g
(needed.)
645
3040
y
Fn
(pars.w)
k
Fl
(
\(
1)
p
Fi
(;)
14
b
Fl
(1
\)
)
p
Fn
(:)
41
b
Fl
(If)
30
b
(step-di
\013
eren)
n
(tiation)
e
(is)
i
(enabled,)
f
(SeDuMi)
i
(w)
n
(eigh)
n
(ts)
d
(the)
i
(relativ)
n
(e)
744
3140
y
(primal,)
f
(dual)
g
(and)
g
(gap)
g
(residuals)
e
(as)
i
(w
\(
1
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:w
\(
2
\)
:1)
g
(in)
g
(order)
f
(to)
h
(
\014
nd)
g
(the)
h
(optimal)
744
3240
y
(step)
e
(di
\013
eren)
n
(tiation.)
37
b
(These)
27
b
(n)
n
(um)
n
(b)
r
(er)
g
(should)
h
(b)
r
(e)
g
(greater)
d
(than)
j
(10)
2966
3210
y
Ff
(
\000
)
p
Fc
(8)
3054
3240
y
Fl
(.)
645
3339
y
Fn
(pars.n)
m
(um)
m
(tol)
j
(
\(
)
p
Fl
(5)
18
b
Fg
(
\002
)
g
Fl
(10)
1435
3309
y
Ff
(
\000
)
p
Fc
(7)
1523
3339
y
Fn
(
\)
,)
32
b
(pars.bign)
m
(um)
m
(tol)
f
(
\(
)
p
Fl
(0)
p
Fi
(:)
p
Fl
(9)
p
Fn
(
\)
,)
f
(pars.n)
m
(umlvl)
i
(
\(
0
\)
:)
41
b
Fl
(These)
744
3439
y
(options)
27
b
(con)
n
(trol)
g
(some)
g
(n)
n
(umerical)
f
(b)
r
(eha)
n
(viour,)
h
(don't)
h
(tamp)
r
(er)
f
(with)
h
(them.)
456
3608
y
(3.2.)
40
b
Fn
(Options)
31
b
(con)
m
(trolling)
g
(the)
h
(prepro)
s
(cessing.)
645
3729
y
(pars.denf)
g
(
\(
10
\)
,)
f
(pars.denq)
h
(
\(
0.75
\)
:)
40
b
Fl
(P)
n
(arameters)
62
b
(used)
j
(in)
g
(deciding)
g
(whic)
n
(h)
744
3829
y
(columns)
28
b
(are)
e
(dense)
i
(and)
f
(sparse.)
645
3929
y
Fn
(pars.free)
k
(
\(
1
\)
:)
42
b
Fl
(Sp)
r
(eci
\014
es)
26
b
(ho)
n
(w)
g
(SeDuMi)
h
(handles)
g
(free)
f
(v)
-5
b
(ariables.)
35
b
(If)
27
b
Fj
(pars.free=0)
744
4028
y
Fl
(then)
41
b
(free)
f
(v)
-5
b
(ariables)
39
b
(are)
g
(con)
n
(v)
n
(erted)
f
(in)
n
(to)
i
(the)
h
(di
\013
erence)
f
(of)
g
(t)
n
(w)
n
(o)
f
(nonnegativ)
n
(e)
744
4128
y
(v)
-5
b
(ariables.)
35
b
(This)
25
b
(metho)
r
(d)
h
(is)
e
(n)
n
(umerically)
h
(unstable)
g
(and)
f
(unnecessarily)
g
(increases)
744
4228
y
(the)
39
b
(n)
n
(um)
n
(b)
r
(er)
g
(of)
f
(v)
-5
b
(ariables.)
69
b
(If)
39
b
Fj
(pars.free=1)
34
b
Fl
(then)
39
b
(free)
f
(v)
-5
b
(ariables)
37
b
(are)
h
(placed)
744
4327
y
(inside)
26
b
(a)
f
(Loren)
n
(tz)
f
(cone)
g
(whose)
h
(
\014
rst)
g
(v)
-5
b
(ariable)
24
b
(is)
h
(unconstrained.)
36
b
(This)
25
b
(metho)
r
(d)
h
(is)
744
4427
y
(more)
j
(stable)
h
(and)
g
(has)
f
(also)
g
(b)
r
(een)
h
(suggested)
f
(b)
n
(y)
h
(Jos)
f
(Sturm)
h
(in)
g
([4].)
44
b
(Please)
29
b
(note)
744
4526
y
(ho)
n
(w)
n
(ev)
n
(er,)
j
(that)
g
(this)
h
(mak)
n
(es)
e
(the)
i
(problem)
f
(nonlinear)
f
(and)
h
(it)
h
(migh)
n
(t)
f
(tak)
n
(e)
g
(longer)
744
4626
y
(to)
c
(solv)
n
(e)
e
(it.)
37
b
(If)
28
b
(y)
n
(ou)
e
(exp)
r
(erience)
h
(suc)
n
(h)
g
(b)
r
(eha)
n
(viour)
f
(then)
i
(c)
n
(hange)
f
(this)
g
(setting)
h
(to)
f
(0.)
645
4726
y
Fn
(pars.sdp)
k
(
\(
1
\)
:)
41
b
Fl
(Enables)
24
b
(the)
i
(SDP)
f
(prepro)
r
(cessing)
e
(routines,)
i
(suc)
n
(h)
g
(as)
f
(detecting)
i
(di-)
744
4825
y
(agonal)
g
(SDP)
i
(blo)
r
(c)
n
(ks.)
456
4994
y
(3.3.)
40
b
Fn
(Options)
30
b
(con)
m
(trolling)
g
(the)
h
(Cholesky)
f
(factorization.)
42
b
Fl
(These)
27
b
(options)
f
(are)
g
(sub-)
456
5094
y
(
\014
elds)
h
(of)
h
Fj
(pars.chol)
p
Fl
(.)
645
5216
y
Fn
(pars.c)
m
(hol.skip)
j
(
\(
1
\)
:)
41
b
Fl
(Enables)
26
b
(skipping)
i
(bad)
f
(piv)
n
(ots.)
p
eop
end
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4
3
bop
456
251
a
Fc
(4)
1256
b
(IMRE)
22
b
(P)
1998
236
y
(
\023
)
1989
251
y
(OLIK)
645
450
y
Fn
(pars.c)
m
(hol.canceltol)
31
b
(
\(
)
p
Fl
(10)
1560
420
y
Ff
(
\000
)
p
Fc
(12)
1681
450
y
Fn
(
\)
:)
42
b
Fl
(Relativ)
n
(e)
g
(tolerance)
g
(for)
h
(detecting)
g
(cancellation)
744
550
y
(during)
27
b
(Cholesky)
g
(factorization.)
645
649
y
Fn
(pars.c)
m
(hol.abstol)
k
(
\(
)
p
Fl
(10)
1443
619
y
Ff
(
\000
)
p
Fc
(20)
1564
649
y
Fn
(
\)
:)
41
b
Fl
(Skips)
28
b
(piv)
n
(ots)
f
(falling)
g
(b)
r
(elo)
n
(w)
g
(this)
h
(v)
-5
b
(alue.)
645
749
y
Fn
(pars.c)
m
(hol.maxuden)
31
b
(
\(
500
\)
:)
41
b
Fl
(Piv)
n
(ots)
46
b
(in)
i
(dense-column)
g
(factorization)
e
(so)
h
(that)
744
849
y
(these)
28
b
(factors)
e
(satisfy)
i
(max
\(
abs
\(
Lk
\)\)
)
f
Fg
(
\024
)
g
Fl
(maxuden.)
456
1048
y
(3.4.)
40
b
Fn
(Options)
c
(con)
m
(trolling)
f
(the)
h
(Conjugate)
h
(Gradien)
m
(t)
g
(re
\014
nemen)
m
(t.)
k
Fl
(V)
-7
b
(arious)
30
b
(pa-)
456
1148
y
(rameters)
19
b
(for)
h
(con)
n
(trolling)
f
(the)
i
(Preconditioned)
e
(conjugate)
h
(gradien)
n
(t)
f
(metho)
r
(d)
i
(
\(
CG
\)
,)
h
(whic)
n
(h)
456
1248
y
(is)
27
b
(only)
g
(used)
h
(if)
g
(results)
f
(from)
g
(Cholesky)
g
(factorization)
f
(are)
h
(inaccurate.)
645
1377
y
Fn
(pars.cg.maxiter)
k
(
\(
49
\)
:)
41
b
Fl
(Maxim)
n
(um)
31
b
(n)
n
(um)
n
(b)
r
(er)
g
(of)
h
(CG-iterates)
e
(
\(
p)
r
(er)
i
(solv)
n
(e
\)
.)
48
b
(The-)
744
1477
y
(oretically)
37
b
(needed)
h
(is)
f
Fj
(|add|+2*|skip|)
p
Fl
(,)
e
(the)
j
(n)
n
(um)
n
(b)
r
(er)
f
(of)
h
(added)
g
(and)
f
(skipp)
r
(ed)
744
1576
y
(piv)
n
(ots)
27
b
(in)
h
(Cholesky)
-7
b
(.)
645
1676
y
Fn
(pars.cg.re
\014
ne)
31
b
(
\(
1
\)
:)
41
b
Fl
(Num)
n
(b)
r
(er)
124
b
(of)
f
(re
\014
nemen)
n
(t)
h
(lo)
r
(ops)
f
(that)
h
(are)
e
(al-)
744
1776
y
(lo)
n
(w)
n
(ed.)
158
b
(The)
68
b
(maxim)
n
(um)
h
(n)
n
(um)
n
(b)
r
(er)
f
(of)
g
(actual)
f
(CG-steps)
h
(will)
h
(th)
n
(us)
f
(b)
r
(e)
744
1875
y
Fj
(1+
\(
1+pars.cg.refi)
o
(ne)
o
(
\)
*p)
o
(ar)
o
(s.c)
o
(g.)
o
(max)
o
(it)
o
(er)
o
Fl
(.)
645
1975
y
Fn
(pars.cg.stagtol)
31
b
(
\(
)
p
Fl
(5)
18
b
Fg
(
\002
)
g
Fl
(10)
1541
1945
y
Ff
(
\000
)
p
Fc
(14)
1662
1975
y
Fn
(
\)
:)
41
b
Fl
(T)
-7
b
(erminates)
30
b
(if)
g
(relativ)
n
(e)
f
(function)
i
(progress)
d
(is)
i
(less)
744
2075
y
(than)
e
(this)
g
(n)
n
(um)
n
(b)
r
(er.)
645
2174
y
Fn
(pars.cg.restol)
i
(
\(
)
p
Fl
(5)
18
b
Fg
(
\002
)
g
Fl
(10)
1492
2144
y
Ff
(
\000
)
p
Fc
(3)
1581
2174
y
Fn
(
\)
:)
41
b
Fl
(T)
-7
b
(erminates)
24
b
(if)
i
(residual)
f
(is)
g
(a)
g
Fj
(pars.cg.restol)
19
b
Fl
(frac-)
744
2274
y
(tion)
k
(of)
f
(the)
h
(dualit)
n
(y)
f
(gap.)
34
b
(Should)
23
b
(b)
r
(e)
g
(smaller)
e
(than)
h
(1)
g
(in)
h
(order)
e
(to)
h
(mak)
n
(e)
g
(progress.)
645
2373
y
Fn
(pars.cg.qprec)
32
b
(
\(
1
\)
:)
41
b
Fl
(Stores)
117
b
(CG-iterates)
f
(in)
i
(quadruple)
f
(precision)
f
(if)
744
2473
y
Fj
(pars.cg.qprec=1)
p
Fl
(.)
456
2673
y
(3.5.)
40
b
Fn
(Debugging)
31
b
(options.)
645
2802
y
(pars.vplot)
g
(
\(
0
\)
:)
41
b
Fl
(If)
32
b
(this)
g
(
\014
eld)
f
(is)
g
(1,)
h
(then)
g
(SeDuMi)
g
(pro)
r
(duces)
f
(a)
g
(plot)
g
(for)
g
(researc)
n
(h)
744
2902
y
(purp)
r
(oses.)
645
3002
y
Fn
(pars.stopat)
h
(
\(
-1
\)
:)
40
b
Fl
(SeDuMi)
26
b
(en)
n
(ters)
e
(debugging)
g
(mo)
r
(de)
h
(at)
f
(the)
h
(iterations)
f
(sp)
r
(eci
\014
ed)
744
3101
y
(in)
k
(this)
g
(v)
n
(ector.)
645
3201
y
Fn
(pars.errors)
k
(
\(
0
\)
:)
41
b
Fl
(If)
35
b
Fj
(pars.errors=1)
29
b
Fl
(then)
36
b
(SeDuMi)
f
(outputs)
g
(some)
f
(error)
f
(mea-)
744
3301
y
(sures)
e
(as)
f
(outlined)
i
(at)
f
(the)
g
(7th)
g
(DIMA)
n
(CS)
h
(c)
n
(hallenge.)
47
b
(The)
31
b
(errors)
e
(are)
h
(b)
r
(oth)
i
(dis-)
744
3400
y
(pla)
n
(y)
n
(ed)
27
b
(in)
h
(the)
g
(output)
g
(and)
f
(returned)
g
(in)
h
Fj
(info.err)
p
Fl
(.)
1572
3641
y
(4.)
41
b
Fk
(Output)
32
b
(f)
n
(orma)
-6
b
(t)
456
3791
y
Fl
(4.1.)
40
b
Fn
(Description)
27
b
(of)
h
(the)
g
(output)
g
(
\014
elds.)
40
b
Fl
(When)
24
b
(calling)
g
(SeDuMi)
h
(with)
f
(three)
g
(output)
456
3890
y
(v)
-5
b
(ariables)
34
b
(
\(
)
p
Fj
([x,y,info]=sedumi)
o
(
\(
.)
o
(..
\)
)
o
Fl
(
\)
)
c
(some)
35
b
(useful)
h
(information)
f
(is)
h
(returned)
f
(in)
h
(the)
456
3990
y
(structure)
27
b
Fj
(info)
p
Fl
(.)
35
b
(It)
28
b
(has)
f
(the)
h
(follo)
n
(wing)
e
(
\014
elds:)
645
4120
y
Fn
(info.cpusec:)
40
b
Fl
(T)
-7
b
(otal)
28
b
(CPU)
g
(
\(
not)
h
(w)
n
(all)
f
(clo)
r
(c)
n
(k
\)
)
g
(time)
h
(in)
g
(seconds)
f
(sp)
r
(en)
n
(t)
g
(in)
h
(optimiza-)
744
4219
y
(tion.)
645
4319
y
Fn
(info.timing:)
38
b
Fl
(Detailed)
31
b
(CPU)
f
(timing)
h
(information)
f
(in)
g
(seconds.)
45
b
(The)
30
b
(three)
h
(n)
n
(um-)
744
4419
y
(b)
r
(ers)
c
(giv)
n
(e)
f
(the)
i
(time)
g
(sp)
r
(en)
n
(t)
f
(in)
h
(prepro)
r
(cessing,)
d
(IPM)
i
(iterations)
f
(and)
h
(p)
r
(ostpro)
r
(cess-)
744
4518
y
(ing,)
35
b
(resp)
r
(ectiv)
n
(ely)
-7
b
(.)
54
b
(Although)
33
b
(in)
h
(most)
f
(cases)
f
(IPM)
h
(iterations)
g
(tak)
n
(e)
g
(more)
f
(than)
744
4618
y
(90
\045
)
27
b
(of)
h
(the)
g
(time,)
g
(in)
g
(some)
f
(cases)
f
(it)
i
(can)
g
(b)
r
(e)
g
(as)
e
(lo)
n
(w)
h
(as)
g
(50
\045
.)
645
4717
y
Fn
(info.feasratio:)
40
b
Fl
(The)
f
(
\014
nal)
g
(v)
-5
b
(alue)
39
b
(of)
g
(the)
h
(feasibilit)
n
(y)
f
(indicator.)
70
b
(This)
39
b
(indicator)
744
4817
y
(con)
n
(v)
n
(erges)
28
b
(to)
j
(1)
f
(for)
h
(problems)
f
(with)
h
(a)
f
(complemen)
n
(tary)
g
(solution,)
h
(and)
f
(to)
h
(-1)
f
(for)
744
4917
y
(strongly)
25
b
(infeasible)
i
(problems.)
35
b
(If)
27
b
Fj
(info.feasratio)
21
b
Fl
(is)
26
b
(somewhere)
f
(in)
h
(b)
r
(et)
n
(w)
n
(een,)
744
5016
y
(and)
i
(the)
g
(problem)
g
(is)
g
(not)
g
(purely)
f
(linear)
g
(then)
i
(the)
f
(problem)
g
(ma)
n
(y)
f
(b)
r
(e)
h
(nast)
n
(y)
g
(
\(
e.g.,)
744
5116
y
(the)
h
(optim)
n
(um)
f
(is)
g
(not)
f
(attained
\)
.)
38
b
(Otherwise,)
28
b
(if)
g
(the)
g
(problem)
g
(is)
g
(linear)
f
(then)
h
(the)
744
5216
y
(reason)
e
(m)
n
(ust)
i
(lie)
g
(in)
g
(n)
n
(umerical)
e
(problems:)
36
b
(try)
28
b
(to)
f
(rescale)
f
(the)
i
(problem.)
p
eop
end
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begin
5
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2363
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2446
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546
2529
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19
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(h,)
546
2612
y
(August)
24
b
(2002.)
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2768
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(University,)
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(Lab)
555
2851
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Fd
(E-mail)
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(addr)
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5
b
Fm
(:)
33
b
Fa
(poliki@mcmaster.ca)
p
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