SeDuMi_Guide_105R5.ps
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SeDuMi_Guide_105R5.ps
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	%%Page: 15 15
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	DO
	SO
	6 w
	0 sg
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	898 388 mt 6254 388 L
	898 2170 mt 898 388 L
	6254 2170 mt 6254 388 L
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	1758 2316 mt
	(2) s
	2683 2170 mt 2683 2116 L
	2683 388 mt 2683 442 L
	2650 2316 mt
	(4) s
	3576 2170 mt 3576 2116 L
	3576 388 mt 3576 442 L
	3543 2316 mt
	(6) s
	4469 2170 mt 4469 2116 L
	4469 388 mt 4469 442 L
	4436 2316 mt
	(8) s
	5361 2170 mt 5361 2116 L
	5361 388 mt 5361 442 L
	5295 2316 mt
	(10) s
	6254 2170 mt 6254 2116 L
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	6188 2316 mt
	(12) s
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	6254 2170 mt 6200 2170 L
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	(0) s
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	(0.5) s
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	(1) s
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	6254 834 mt 6200 834 L
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	(1.5) s
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	(2) s
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	898 388 mt 6254 388 L
	898 2170 mt 898 388 L
	6254 2170 mt 6254 388 L
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 980 5057 823 MR c np
	36 36 898 1279 FO
	36 36 1344 1451 FO
	36 36 1791 1576 FO
	36 36 2237 1664 FO
	36 36 2683 1729 FO
	36 36 3130 1713 FO
	36 36 3576 1374 FO
	36 36 4022 1053 FO
	36 36 4469 1172 FO
	36 36 4915 1606 FO
	36 36 5361 1367 FO
	36 36 5808 1284 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 934 5057 932 MR c np
	36 36 898 1279 FO
	36 36 1344 1355 FO
	36 36 1791 1463 FO
	36 36 2237 1649 FO
	36 36 2683 1752 FO
	36 36 3130 1792 FO
	36 36 3576 1438 FO
	36 36 4022 1007 FO
	36 36 4469 1175 FO
	36 36 4915 1591 FO
	36 36 5361 1359 FO
	36 36 5808 1281 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 865 5057 878 MR c np
	36 36 898 1279 FO
	36 36 1344 1443 FO
	36 36 1791 1449 FO
	36 36 2237 1287 FO
	36 36 2683 1104 FO
	36 36 3130 938 FO
	36 36 3576 1076 FO
	36 36 4022 1669 FO
	36 36 4469 1320 FO
	36 36 4915 1166 FO
	36 36 5361 1191 FO
	36 36 5808 1249 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 877 5057 476 MR c np
	36 36 898 1279 FO
	36 36 1344 1169 FO
	36 36 1791 1147 FO
	36 36 2237 1105 FO
	36 36 2683 1034 FO
	36 36 3130 976 FO
	36 36 3576 1055 FO
	36 36 4022 1013 FO
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	36 36 4915 973 FO
	36 36 5361 950 FO
	36 36 5808 977 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
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	36 36 898 1279 FO
	36 36 1344 1442 FO
	36 36 1791 1704 FO
	36 36 2237 1521 FO
	36 36 2683 1595 FO
	36 36 3130 1791 FO
	36 36 3576 1729 FO
	36 36 4022 1877 FO
	36 36 4469 1466 FO
	36 36 4915 1753 FO
	36 36 5361 1751 FO
	36 36 5808 1583 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 774 5057 1205 MR c np
	36 36 898 1279 FO
	36 36 1344 1431 FO
	36 36 1791 1421 FO
	36 36 2237 1774 FO
	36 36 2683 1905 FO
	36 36 3130 847 FO
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	36 36 4469 1326 FO
	36 36 4915 1155 FO
	36 36 5361 1190 FO
	36 36 5808 1249 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 838 5057 1272 MR c np
	36 36 898 1279 FO
	36 36 1344 911 FO
	36 36 1791 1019 FO
	36 36 2237 969 FO
	36 36 2683 914 FO
	36 36 3130 2036 FO
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	36 36 4915 1536 FO
	36 36 5361 1342 FO
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	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 812 5057 1032 MR c np
	36 36 898 1279 FO
	36 36 1344 1220 FO
	36 36 1791 1250 FO
	36 36 2237 1115 FO
	36 36 2683 1001 FO
	36 36 3130 885 FO
	36 36 3576 1052 FO
	36 36 4022 1770 FO
	36 36 4469 1387 FO
	36 36 4915 1068 FO
	36 36 5361 1164 FO
	36 36 5808 1245 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 890 5057 1139 MR c np
	36 36 898 1279 FO
	36 36 1344 1445 FO
	36 36 1791 1489 FO
	36 36 2237 1754 FO
	36 36 2683 1869 FO
	36 36 3130 1955 FO
	36 36 3576 1505 FO
	36 36 4022 963 FO
	36 36 4469 1164 FO
	36 36 4915 1626 FO
	36 36 5361 1375 FO
	36 36 5808 1284 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 948 5057 921 MR c np
	36 36 898 1279 FO
	36 36 1344 1435 FO
	36 36 1791 1384 FO
	36 36 2237 1274 FO
	36 36 2683 1421 FO
	36 36 3130 1725 FO
	36 36 3576 1021 FO
	36 36 4022 1123 FO
	36 36 4469 1269 FO
	36 36 4915 1645 FO
	36 36 5361 1439 FO
	36 36 5808 1795 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 423 5057 1702 MR c np
	36 36 898 1279 FO
	36 36 1344 755 FO
	36 36 1791 862 FO
	36 36 2237 838 FO
	36 36 2683 820 FO
	36 36 3130 827 FO
	36 36 3576 1932 FO
	36 36 4022 2051 FO
	36 36 4469 1557 FO
	36 36 4915 496 FO
	36 36 5361 1134 FO
	36 36 5808 1129 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 812 5057 1032 MR c np
	36 36 898 1279 FO
	36 36 1344 1220 FO
	36 36 1791 1250 FO
	36 36 2237 1115 FO
	36 36 2683 1001 FO
	36 36 3130 885 FO
	36 36 3576 1052 FO
	36 36 4022 1770 FO
	36 36 4469 1387 FO
	36 36 4915 1068 FO
	36 36 5361 1164 FO
	36 36 5808 1245 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 890 5057 1139 MR c np
	36 36 898 1279 FO
	36 36 1344 1445 FO
	36 36 1791 1489 FO
	36 36 2237 1754 FO
	36 36 2683 1869 FO
	36 36 3130 1955 FO
	36 36 3576 1505 FO
	36 36 4022 963 FO
	36 36 4469 1164 FO
	36 36 4915 1626 FO
	36 36 5361 1375 FO
	36 36 5808 1284 FO

	gr
	gs 898 388 5357 1783 MR c np

	gr
	gs 825 816 5057 867 MR c np
	36 36 898 1279 FO
	36 36 1344 1582 FO
	36 36 1791 889 FO
	36 36 2237 944 FO
	36 36 2683 1148 FO
	36 36 3130 1454 FO
	36 36 3576 1289 FO
	36 36 4022 1145 FO
	36 36 4469 1171 FO
	36 36 4915 1609 FO
	36 36 5361 1369 FO
	36 36 5808 1284 FO

	gr
	gs 898 388 5357 1783 MR c np
	4910 0 898 1279 2 MP stroke
	4910 0 898 1947 2 MP stroke

	gr
	3081 293 mt
	(Wide region v-plot) s
	3334 2459 mt
	(iterations) s
	642 1824 mt -90 rotate
	(normalized v-values) s
	90 rotate
	1 sg
	0 1782 5356 0 0 -1782 898 4612 4 MP
	PP
	-5356 0 0 1782 5356 0 0 -1782 898 4612 5 MP stroke
	4 w
	DO
	SO
	6 w
	0 sg
	898 4612 mt 6254 4612 L
	898 2830 mt 6254 2830 L
	898 4612 mt 898 2830 L
	6254 4612 mt 6254 2830 L
	898 4612 mt 6254 4612 L
	898 4612 mt 898 2830 L
	898 4612 mt 898 4558 L
	898 2830 mt 898 2884 L
	865 4758 mt
	(0) s
	1385 4612 mt 1385 4558 L
	1385 2830 mt 1385 2884 L
	1352 4758 mt
	(1) s
	1872 4612 mt 1872 4558 L
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	1839 4758 mt
	(2) s
	2359 4612 mt 2359 4558 L
	2359 2830 mt 2359 2884 L
	2326 4758 mt
	(3) s
	2846 4612 mt 2846 4558 L
	2846 2830 mt 2846 2884 L
	2813 4758 mt
	(4) s
	3333 4612 mt 3333 4558 L
	3333 2830 mt 3333 2884 L
	3300 4758 mt
	(5) s
	3819 4612 mt 3819 4558 L
	3819 2830 mt 3819 2884 L
	3786 4758 mt
	(6) s
	4306 4612 mt 4306 4558 L
	4306 2830 mt 4306 2884 L
	4273 4758 mt
	(7) s
	4793 4612 mt 4793 4558 L
	4793 2830 mt 4793 2884 L
	4760 4758 mt
	(8) s
	5280 4612 mt 5280 4558 L
	5280 2830 mt 5280 2884 L
	5247 4758 mt
	(9) s
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	5767 2830 mt 5767 2884 L
	5701 4758 mt
	(10) s
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	(11) s
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	(0) s
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	6254 4256 mt 6200 4256 L
	697 4300 mt
	(0.2) s
	898 3899 mt 952 3899 L
	6254 3899 mt 6200 3899 L
	697 3943 mt
	(0.4) s
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	6254 3543 mt 6200 3543 L
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	(0.6) s
	898 3186 mt 952 3186 L
	6254 3186 mt 6200 3186 L
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	(0.8) s
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	(1) s
	898 4612 mt 6254 4612 L
	898 2830 mt 6254 2830 L
	898 4612 mt 898 2830 L
	6254 4612 mt 6254 2830 L
	gs 898 2830 5357 1783 MR c np
	487 -36 487 -46 487 349 487 -215 487 -94 486 48 487 263 487 132
	487 -1 487 249 1385 3875 11 MP stroke

	gr
	3159 2735 mt
	(Reduction rates) s
	3334 4901 mt
	(iterations) s
	642 4085 mt -90 rotate
	(reduction rate) s
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	3307 y($optional$)30 b(\014elds:)164 3495 y Fl(K.f)f
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	b(ariables,)29 b(i.e.)41 b(the)31 b(n)m(um)m(b)s(er)e(of)h(dual)f
	(equalit)m(y)h(constrain)m(ts)164 3682 y Fl(K.l)f Fp(The)h(n)m(um)m(b)s
	(er)f(of)i(nonnegativit)m(y)f(constrain)m(ts)164 3870
	y Fl(K.q)f Fp(A)i(list)e(of)h(dimensions)e(of)i(quadratic)g(cone)h
	(constrain)m(ts)164 4058 y Fl(K.r)e Fp(A)i(list)e(of)h(dimensions)e(of)
	i(rotated)i(quadratic)e(cone)h(constrain)m(ts)164 4245
	y Fl(K.xcomplex)23 b Fp(A)j(list)e(of)i(primal)e(v)-5
	b(ariables)24 b(in)h(the)h Fl(f,l,q,r)e Fp(blo)s(c)m(ks)h(that)h(are)h
	(allo)m(w)m(ed)e(to)i(ha)m(v)m(e)g(a)f(nonzero)345 4358
	y(imaginary)g(part.)40 b(The)27 b(imaginary)f(parts)h(of)g(the)g(asso)s
	(ciated)h(dual)e(constrain)m(ts)h(are)h(then)f(explicitly)345
	4471 y(restricted.)164 4659 y Fl(K.s)i Fp(A)i(list)e(of)h(orders)g(of)g
	(p)s(ositiv)m(e)g(semide\014niteness)e(constrain)m(ts)164
	4846 y Fl(K.scomplex)23 b Fp(A)j(list)f(of)i(matrix)f(v)-5
	b(ariables)25 b(that)h(are)h(restricted)f(to)h(b)s(e)f(Hermitian)f(p)s
	(ositiv)m(e)g(semide\014nite.)1962 5225 y(27)p eop
	%%Page: 28 28
	28 27 bop 164 573 a Fl(K.ycomplex)29 b Fp(This)i(\014eld)h(is)f(not)i
	(related)g(to)g Fk(K)q Fp(.)48 b(It)33 b(lists)e(the)i(comp)s(onen)m
	(ts)g(of)g(the)f Fj(y)s Fp(-v)-5 b(ariables)32 b(that)h(are)345
	686 y(complex)c(v)-5 b(alued.)39 b(Equiv)-5 b(alen)m(tly)d(,)28
	b(it)g(lists)g(the)h(primal)d(equalit)m(y)j(constrain)m(ts)g(\()p
	Fj(Ax)p Fp(\))3277 700 y Ff(i)3331 686 y Fp(=)c Fj(b)3466
	700 y Ff(i)3523 686 y Fp(that)k(ha)m(v)m(e)345 799 y(to)i(b)s(e)f
	(satis\014ed)g(not)g(only)g(in)f(their)g(real)h(parts,)h(but)e(also)i
	(in)e(their)g(imaginary)g(parts.)118 982 y(The)h(structure)g
	Fl(K)g Fp(de\014nes)f Fk(K)j Fp(to)f(b)s(e)200 1181 y
	Fk(K)c Fp(=)e Fk(<)458 1143 y Fc(K)p Ff(:)p Fc(f)572
	1181 y Fk(\002)20 b(<)729 1143 y Fc(K)p Ff(:)p Fc(l)729
	1203 y Fh(+)843 1181 y Fk(\002)g Fp(\(Qcone)h Fk(\002)f(\001)15
	b(\001)g(\001)21 b(\002)f Fp(Qcone)q(\))g Fk(\002)g Fp(\(Rcone)h
	Fk(\002)f(\001)15 b(\001)g(\001)22 b(\002)e Fp(Rcone\))h
	Fk(\002)f Fp(\(Scone)h Fk(\002)e(\001)c(\001)g(\001)22
	b(\002)e Fp(Scone\))p Fj(;)118 1380 y Fp(In)47 b(total,)52
	b(the)c(n)m(um)m(b)s(er)e(of)h(Qcone)h($Rcone)q(,)j(Scone)q($)c(comp)
	s(onen)m(ts)h(is)e Fl(length$K.q$)e Fp($)p Fl(length\(K.r$)p
	Fp(,)118 1492 y Fl(length$K.s$)p Fp(\).)38 b(The)30
	b Fj(i)p Fp(th)g(Qcone)h(is)1069 1691 y(Qcone)1317 1713
	y Ff(i)1370 1691 y Fp(=)25 b Fk(f)p Fp(\()p Fj(x)1598
	1705 y Fh(1)1638 1691 y Fj(;)15 b(x)1730 1705 y Fh(2)1770
	1691 y Fp(\))26 b Fk(2)e(<)c(\002)g(C)2146 1654 y Fc(K)p
	Ff(:)p Fc(q)p Fh([)p Fc(i)p Fh(])p Ft(\000)p Fh(1)2431
	1691 y Fk(j)25 b Fj(x)2533 1705 y Fh(1)2598 1691 y Fk(\025)g(k)p
	Fj(x)2791 1705 y Fh(2)2831 1691 y Fk(kg)p Fj(;)118 1890
	y Fp(where)30 b Fk(C)434 1857 y Ff(n)511 1890 y Fp(denotes)h(the)g
	(space)g(of)f(complex)g Fj(n)p Fp({tuples.)40 b(The)30
	b Fj(j)5 b Fp(th)31 b(Rcone)g(is)543 2125 y(Rcone)787
	2139 y Ff(j)849 2125 y Fp(=)945 2006 y Fe(\032)1007 2125
	y Fp(\()p Fj(x)1094 2139 y Fh(1)1134 2125 y Fj(;)15 b(x)1226
	2139 y Fh(2)1266 2125 y Fj(;)g(x)1358 2139 y Fh(3)1397
	2125 y Fp(\))26 b Fk(2)f(<)20 b(\002)g(<)g(\002)f(C)1950
	2087 y Fc(K)p Ff(:)p Fc(r)p Fh([)p Fc(j)p Fh(])p Ft(\000)p
	Fh(2)2225 2002 y Fe(\014)2225 2052 y(\014)2225 2102 y(\014)2225
	2152 y(\014)2252 2125 y Fj(x)2304 2139 y Fh(1)2344 2125
	y Fj(x)2396 2139 y Fh(2)2460 2125 y Fk(\025)2566 2063
	y Fp(1)p 2566 2103 46 4 v 2566 2187 a(2)2622 2125 y Fk(k)p
	Fj(x)2719 2139 y Fh(3)2759 2125 y Fk(k)2804 2087 y Fh(2)2844
	2125 y Fj(;)30 b(x)2951 2139 y Fh(1)3011 2125 y Fp(+)20
	b Fj(x)3154 2139 y Fh(2)3218 2125 y Fk(\025)25 b Fp(0)3370
	2006 y Fe(\033)3447 2125 y Fj(;)118 2359 y Fp(and)30
	b(the)g Fj(k)s Fp(th)h(Scone)f(is)680 2558 y(Scone)907
	2573 y Ff(k)975 2558 y Fp(=)1071 2464 y Fe(n)1127 2558
	y Fj(x)25 b Fk(2)g(C)1343 2520 y Fc(K)p Ff(:)p Fc(s)p
	Fh([)p Fc(k)p Fh(])1508 2497 y Fa(2)1567 2558 y Fk(j)h
	Fl(mat)p Fp($)p Fl(x)p Fp($)k(is)f(Hermitian)g(p)s(ositiv)m(e)h
	(semide\014nite)3240 2464 y Fe(o)3310 2558 y Fj(;)118
	2782 y Fp(for)e(primal)d(comp)s(onen)m(ts.)41 b(F)-8
	b(or)28 b(dual)f(comp)s(onen)m(ts)h Fj(z)h Fp(=)c Fj(c)16
	b Fk(\000)f Fj(A)2310 2749 y Fh(T)2365 2782 y Fj(y)s
	Fp(,)29 b(w)m(e)f(use)g(a)g(sligh)m(tly)e(milder)g(de\014nition)f(of)
	118 2895 y(Scone,)31 b(viz.)701 3105 y(Scone)928 3120
	y Ff(k)996 3105 y Fp(=)1092 3011 y Fe(n)1147 3105 y Fj(z)f
	Fk(2)25 b(C)1358 3067 y Fc(K)p Ff(:)p Fc(s)p Fh([)p Fc(k)p
	Fh(])1523 3044 y Fa(2)1583 3105 y Fk(j)g Fl(mat)p Fp(\()p
	Fl(z)p Fp(\))20 b(+)g Fl(mat)p Fp($)p Fl(z)p Fp($)2268
	3067 y Ft(0)2321 3105 y Fp(is)30 b(p)s(ositiv)m(e)f(semide\014nite)3219
	3011 y Fe(o)3290 3105 y Fj(:)118 3314 y Fp(If)h Fj(k)k
	Fp(is)29 b Fo(not)i Fp(listed)e(in)g Fl(K.scomplex)p
	Fp(,)f(then)i(the)g(de\014nition)e(in)i(the)g(dual)f(is)h(ev)m(en)h
	(milder,)d(namely)-8 b(,)622 3526 y(Scone)849 3541 y
	Ff(k)917 3526 y Fp(=)1013 3432 y Fe(n)1069 3526 y Fj(z)29
	b Fk(2)c(C)1279 3488 y Fc(K)p Ff(:)p Fc(s)p Fh([)p Fc(k)p
	Fh(])1444 3465 y Fa(2)1504 3526 y Fk(j)50 b Fp(Re)26
	b Fl(mat)p Fp($)p Fl(z)p Fp($)20 b(+)g Fl(mat)p Fp(\()p
	Fl(z)p Fp(\))2347 3488 y Ft(0)2400 3526 y Fp(is)29 b(p)s(ositiv)m(e)h
	(semide\014nite)3298 3432 y Fe(o)3368 3526 y Fj(:)118
	3735 y Fp(The)g(length)g(of)g(the)h(v)m(ector)h Fj(c)e
	Fp(should)f(b)s(e)214 3919 y Fl(length$c$)45 b(=)i(K.f)g(+)h(K.l)f(+)
	g(sum$K.q$)f(+)h(sum$K.r$)f(+)h(sum$K.s.^2$)118
	4102 y Fp(If)30 b(the)h(data)g(\()p Fj(A;)15 b(b;)g(c)p
	Fp(\))32 b(is)d(real)h(v)-5 b(alued,)30 b(then)g Fj(x)g
	Fp(and)g Fj(y)j Fp(will)28 b(also)i(b)s(e)g(real)g(v)-5
	b(alued.)259 4215 y(The)30 b(parameter)h Fl(pars)e Fp(is)h(a)g(MA)-8
	b(TLAB)32 b(structure,)e(consisting)f(of)i(the)f(follo)m(wing)f
	($optional$)h(\014elds:)164 4398 y Fl(pars.fid)35 b
	Fp(By)k(default,)h Fl(pars.fid=1)p Fp(,)d(whic)m(h)g(tells)g
	Fl(SeDuMi)g Fp(to)i(pro)s(duce)e(iterativ)m(e)h(statistics)g(on)g(the)
	345 4511 y(screen.)i(If)28 b Fl(pars.fid=0)p Fp(,)e(then)h
	Fl(SeDuMi)g Fp(runs)f(quietly)-8 b(,)28 b(i.e.)g(no)g(screen)g(output.)
	39 b(In)27 b(general,)i(output)345 4624 y(is)g(written)f(to)i(the)f
	(\014le)f(or)h(device)g(that)h(is)e(iden)m(ti\014ed)f(b)m(y)i(the)h
	(\014le)e(handle)g Fl(pars.fid)p Fp(.)38 b(A)29 b(\014le)f(handle)345
	4737 y(is)i(assigned)f(to)j(a)e(\014le)g(b)m(y)g(the)h(MA)-8
	b(TLAB)31 b(function)e Fl(fopen)p Fp(,)g(as)i(in)393
	4956 y Fl(pars.fid)46 b(=)h(fopen$'truss1.out','w'$.)1962
	5225 y Fp(28)p eop
	%%Page: 29 29
	29 28 bop 164 573 a Fl(pars.alg)28 b Fp(By)j(default,)f
	Fl(pars.alg=2)p Fp(.)39 b(If)30 b Fl(pars.alg=0)p Fp(,)f(then)h(a)h
	(\014rst-order)f(algorithm)g(is)g(used,)g(whic)m(h)345
	686 y(is)e(not)h(recommendable.)39 b(If)28 b Fl(pars.alg=1)p
	Fp(,)f(then)h Fl(SeDuMi)f Fp(uses)h(the)g(cen)m
	(tering-predictor-corrector)345 799 y(algorithm)20 b(with)g
	Fj(v)s Fp(-linearization.)36 b(If)20 b Fl(pars.alg=2)f
	Fp(then)h Fj(xz)t Fp(-linearization)g(is)f(used)i(in)e(the)i
	(corrector,)345 912 y(similar)i(to)j(Mehrotra's)g(algorithm.)38
	b(All)24 b(3)h(algorithms)f(are)i(sp)s(ecial)e(instances)h(of)g(the)g
	(generic)h(wide-)345 1024 y(region)k(algorithm,)g(as)h(discussed)d(in)h
	(Chapter)h(7)h(of)f(Sturm)f([25)q(].)164 1210 y Fl(pars.theta,)44
	b(pars.beta)36 b Fp(By)i(default,)h Fl(pars.theta=0.25)34
	b Fp(and)j Fl(pars.beta=0.5)p Fp(.)60 b(These)38 b(are)g(the)345
	1323 y(wide)30 b(region)f(and)h(neigh)m(b)s(orho)s(o)s(d)e(parameters.)
	41 b(V)-8 b(alid)30 b(c)m(hoices)h(are)f(0)c Fj(<)f(\022)j(<)p
	Fp(=)c(1)31 b(and)f(0)25 b Fj(<)g(\014)31 b(<)25 b Fp(1.)164
	1509 y Fl(pars.stepdif,)44 b(pars.w)30 b Fp(By)i(default,)f
	Fl(pars.stepdif=1)d Fp(and)j Fl(pars.w)46 b(=)i([1)f(1])p
	Fp(.)d(This)30 b(means)i(that)345 1622 y(primal/dual)27
	b(step)j(length)f(di\013eren)m(tiation)g(is)g(enabled)g(\(disabled)f
	(if)h Fl(pars.stepdif=0)p Fp(\).)37 b(The)29 b(pri-)345
	1735 y(orities)24 b(of)h(the)f(relativ)m(e)h(primal,)f(dual)f(and)h
	(gap)g(residuals)f(are)h(w)m(eigh)m(ted)h(as)g Fl(w$1$:w$2$:1)p
	Fp(,)e(in)g(order)345 1848 y(to)31 b(\014nd)e(the)i(optimal)e(step)i
	(di\013eren)m(tiation.)164 2034 y Fl(pars.vplot)38 b
	Fp(If)j(this)f(\014eld)g(is)g(1,)45 b(then)c(SeDuMi)g(pro)s(duces)f(a)h
	(fancy)h Fj(v)s Fp(-plot,)i(for)d(researc)m(h)h(purp)s(oses.)345
	2147 y(Default:)f Fl(vplot)47 b(=)g(0)p Fp(.)164 2333
	y Fl(pars.eps)28 b Fp(The)i(desired)e(accuracy)-8 b(.)164
	2518 y Fl(pars.bigeps)27 b Fp(The)j(required)e(accuracy)k(to)f(get)g
	Fl(info.numerr)45 b(<)j(2)p Fp(.)164 2704 y Fl(pars.maxiter)27
	b Fp(Maxim)m(um)i(n)m(um)m(b)s(er)g(of)i(iterations,)f(b)s(efore)g
	(termination.)164 2890 y Fl(pars.denq)f Fp(Prop)s(ortion)i(of)h
	(x$i$'s)g(for)g(whic)m(h)f(the)h(sparsit)m(y)f(in)g(A$:,i$)h(is)g
	(considered)e(normal.)45 b(Default:)345 3003 y(0.75.)164
	3189 y Fl(pars.denf)23 b Fp(A)j(column)f(is)h(treated)h(as)f(dense)g
	(if)f(it)h(has)g Fl(pars.denf)d Fp(times)j(more)g(nonzeros)g(than)g
	(normal.)345 3302 y(Default:)41 b(10.)164 3488 y Fl(pars.stopat)34
	b Fp(En)m(ters)k(MA)-8 b(TLAB)39 b(debugging)e(mo)s(de)h(at)g(the)h(b)s
	(eginning)c(of)j(iteration)f Fl(pars.stopat)p Fp(.)345
	3601 y(Default:)k(-1.)164 3786 y Fl(pars.cg)k Fp(V)-8
	b(arious)47 b(parameters)g(for)g(con)m(troling)g(the)g(Preconditioned)f
	(conjugate)i(gradien)m(t)f(metho)s(d)345 3899 y($CG$,)c(whic)m(h)d
	(is)g(only)h(used)g(if)f(results)g(from)h(Cholesky)g(are)h(inaccurate.)
	74 b(T)m(yp)s(e)41 b(`help)f(sedumi')345 4012 y(for)31
	b(details.)164 4198 y Fl(pars.chol)18 b Fp(V)-8 b(arious)20
	b(parameters)h(for)g(con)m(troling)f(the)h(Cholesky)f(solv)m(e.)38
	b(T)m(yp)s(e)20 b(`help)g(sedumi')f(for)h(details.)259
	4381 y(The)30 b(output)g(parameter)h Fl(info)e Fp(is)h(a)g(MA)-8
	b(TLAB)32 b(structure,)e(with)f(the)h(follo)m(wing)f(\014elds:)164
	4565 y Fl(info.pinf)f Fp(and)j Fl(info.dinf)d Fp(The)j(feasibilit)m(y)e
	(status)i(of)g(the)g(primal-dual)d(problem)i(pair,)g(as)h(detected)345
	4678 y(b)m(y)g Fl(SeDuMi)p Fp(.)39 b(There)30 b(are)g(three)h(cases:)
	429 4863 y(1.)46 b Fl(pinf)h(=)g(dinf)g(=)h(0)36 b Fp(Then)h
	Fj(x)g Fp(and)f Fj(y)k Fp(are)e($appro)m(ximate$)g(optimal)e
	(solutions,)i(i.e.)f Fj(Ax)g Fp(=)f Fj(b)p Fp(,)545 4976
	y Fj(x)26 b Fk(2)e(K)q Fp(,)32 b Fj(c)20 b Fk(\000)g
	Fj(A)1053 4943 y Fh(T)1108 4976 y Fj(y)28 b Fk(2)d(K)q
	Fp(,)31 b(and)f Fj(c)1609 4943 y Fh(T)1665 4976 y Fj(x)25
	b Fk(\024)g Fj(b)1877 4943 y Fh(T)1932 4976 y Fj(y)33
	b Fp($appro)m(ximately$.)1962 5225 y(29)p eop
	%%Page: 30 30
	30 29 bop 429 573 a Fp(2.)46 b Fl(pinf)h(=)g(1)35 b Fp(Primal)f(is)g
	(infeasible,)g(i.e.)h Fk(f)p Fj(x)f Fk(2)f(K)i(j)e Fj(Ax)h
	Fp(=)f Fj(b)p Fk(g)h Fp(=)f Fk(;)p Fp(.)55 b(Then)34
	b Fj(y)k Fp(is)c(a)i(F)-8 b(ark)j(as-t)m(yp)s(e)545 686
	y(solution,)30 b(i.e.)g Fj(b)1100 653 y Fh(T)1155 686
	y Fj(y)e(>)d Fp(0)31 b(and)f Fk(\000)p Fj(A)1716 653
	y Fh(T)1771 686 y Fj(y)e Fk(2)d(K)q Fp(.)429 832 y(3.)46
	b Fl(dinf)h(=)g(1)35 b Fp(Dual)g(is)g(infeasible,)f(i.e.)h
	Fk(f)p Fj(y)i Fk(j)c Fj(c)24 b Fk(\000)f Fj(A)2274 799
	y Fh(T)2330 832 y Fj(y)36 b Fk(2)d(K)q(g)h Fp(=)f Fk(;g)p
	Fp(.)57 b(Then)34 b Fj(x)h Fp(is)f(a)i(F)-8 b(ark)j(as-t)m(yp)s(e)545
	945 y(solution,)30 b(i.e.)g Fj(c)1100 912 y Fh(T)1156
	945 y Fj(x)25 b(<)g Fp(0,)31 b Fj(Ax)25 b Fp(=)g(0)31
	b(and)f Fj(x)25 b Fk(2)g(K)q Fp(.)164 1132 y Fl(info.numerr)g
	Fp(A)j(p)s(ositiv)m(e)g(v)-5 b(alue)27 b(of)i Fl(info.numerr)c
	Fp(means)j(that)h Fl(SeDuMi)e Fp(terminated)h(without)f(ac)m(hiev-)345
	1245 y(ing)37 b(the)g(desired)e(accuracy)-8 b(,)41 b(b)s(ecause)c(of)g
	(n)m(umerical)f(problems.)59 b(If)37 b Fl(info.numerr)44
	b(=)k(1)37 b Fp(then)f(the)345 1358 y(results)42 b(are)h(merely)f
	(inaccurate:)66 b(the)43 b(solution)f(has)g(still)f(ac)m(hiev)m(ed)j
	(the)f(accuracy)h(denoted)f(b)m(y)345 1471 y Fl(pars.bigeps)p
	Fp(,)e(whic)m(h)e(is)g Fl(1E-3)h Fp(b)m(y)g(default.)70
	b(If)40 b Fl(info.numerr)45 b(=)j(2)40 b Fp(then)g Fl(SeDuMi)f
	Fp(failed)g(com-)345 1584 y(pletely)-8 b(.)1962 5225
	y(30)p eop
	%%Trailer
	end
	userdict /end-hook known{end-hook}if
	%%EOF

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