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%%Page: 19 19
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%%Page: 20 20
20 19 bop 261 573 a Fl(3.0000)46 b(+)i(1.0000i)141 b(0.8000)46
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%%Page: 21 21
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22 21 bop 118 573 a Fp(A)34 b(similar)e(con)m(v)m(en)m(tion)j(holds)e
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5701 4758 mt
(10) s
6254 4612 mt 6254 4558 L
6254 2830 mt 6254 2884 L
6188 4758 mt
(11) s
898 4612 mt 952 4612 L
6254 4612 mt 6200 4612 L
797 4656 mt
(0) s
898 4256 mt 952 4256 L
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
898 3543 mt 952 3543 L
6254 3543 mt 6200 3543 L
697 3587 mt
(0.6) s
898 3186 mt 952 3186 L
6254 3186 mt 6200 3186 L
697 3230 mt
(0.8) s
898 2830 mt 952 2830 L
6254 2830 mt 6200 2830 L
797 2874 mt
(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
90 rotate
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2818 y(v)-5 b(alues,)27 b(whereas)f Fl(pars.alg)46 b(=)h(2)26
b Fp(uses)g(linearization)e(of)j(the)g(squared)e Fj(v)s
Fp(-v)-5 b(alues,)28 b(whic)m(h)d(is)g(also)h(kno)m(wn)g(as)118
2931 y Fj(xz)t Fp(-linearization.)39 b(F)-8 b(or)29 b(linear)f
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%%Page: 24 24
24 23 bop 118 573 a Fp(threshold)28 b(will)e(b)s(e)i(corrected)j(b)m(y)
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25 24 bop 164 573 a Fp([5])46 b(S.)37 b(Deng)h(and)e(H.)i(Hu.)60
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799 y(USA,)30 b(1996.)164 977 y([6])46 b(S.)33 b(Dussy)f(and)g(L.)h(El)
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1269 y([7])46 b(L.)38 b(El)f(Ghaoui)h(and)f(H.)i(Lebret.)63
b(Robust)38 b(solutions)e(to)j(least-squares)g(problems)d(with)h
(uncertain)305 1382 y(data.)k Fo(SIAM)32 b(Journal)i(on)f(Matrix)g(A)n
(nalysis)g(and)g(Applic)-5 b(ations)p Fp(,)33 b(18\(4\):1035{1064,)k
(1997.)164 1561 y([8])46 b(L.)36 b(El)f(Ghaoui,)h(R.)g(Nik)m(oukhah,)h
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b(Dualit)m(y)34 b(and)f(self-dualit)m(y)f(for)i(conic)g(con)m(v)m(ex)h
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4863 y([17])47 b(S.)23 b(Mehrotra.)31 b(On)23 b(the)h(implemen)m
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(d.)30 b Fo(SIAM)c(Journal)305 4976 y(on)33 b(Optimization)p
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26 25 bop 118 573 a Fp([18])47 b(S.)34 b(Mehrotra)h(and)e(Y.)i(Y)-8
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873 y([19])47 b(H.D.)140 b(Mittelmann.)365 b(Sev)m(eral)139
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b(Y.)40 b(Nestero)m(v)h(and)d(M.J.)i(T)-8 b(o)s(dd.)66
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b(-)h(CNRS,)f(T)-8 b(oulouse,)54 b(F)-8 b(rance.)100
b(Av)-5 b(ailable)48 b(from)305 2114 y Fl(http://www.laas.fr/)43
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b Fo(The)-5 b(ory)38 b(and)g(algorithms)i(for)d(line)-5
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2527 y(Sons,)30 b(New)g(Y)-8 b(ork,)32 b(1997.)118 2715
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b(1998.)118 3015 y([25])47 b(J.F.)37 b(Sturm.)57 b Fo(Primal{Dual)40
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b(o)g(gr)g(amming)p Fp(,)41 b(v)m(olume)305 3128 y(156)e(of)g
Fo(Tinb)-5 b(er)g(gen)40 b(Institute)g(R)-5 b(ese)g(ar)g(ch)41
b(Series)p Fp(.)64 b(Thesis)37 b(Publishers,)f(Amsterdam,)k(The)e
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b(and)f(R.H.)i(T)s(\177)-48 b(ut)s(\177)g(unc)s(\177)g(u.)49
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b(ec)m(hnical)26 b(rep)s(ort,)g(Sc)m(ho)s(ol)f(of)i(Op)s(erations)d
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y(Cornell)28 b(Univ)m(ersit)m(y)-8 b(,)31 b(Ithaca,)g(NY,)g(USA,)g
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27 26 bop 118 573 a Fp([30])47 b(S.)24 b(W)-8 b(u,)27
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29 28 bop 164 573 a Fl(pars.alg)28 b Fp(By)j(default,)f
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(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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