Algorithms and Software for LMI Problems in Control Introduction
Algorithms and Software for LMI Problems in Control Introduction
Algorithms and Software for LMI Problems in Control Introduction
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
[23]I.Dik<strong>in</strong>,\Iterativesolutionofproblemsofl<strong>in</strong>ear<strong>and</strong>quadraticprogramm<strong>in</strong>g",SovietMath. [24]N.Karmarkar,\Anewpolynomial-timealgorithm<strong>for</strong>l<strong>in</strong>earprogramm<strong>in</strong>g",Comb<strong>in</strong>atorica, vol.4,pp.373{395,1984. Dokl.,vol.8,pp.674{675,1967.<br />
[25]Yu.Nesterov<strong>and</strong>A.Nemirovsky,\Ageneralapproachtopolynomial-timealgorithmsdesign<br />
[26]F.Alizadeh,\Optimizationoverthepositive-denitecone:<strong>in</strong>teriorpo<strong>in</strong>tmethods<strong>and</strong>com- <strong>for</strong>convexprogramm<strong>in</strong>g",Technicalreport,Centr.Econ.&Math.Inst.,USSRAcad.Sci.,<br />
b<strong>in</strong>atorialapplications",<strong>in</strong>PanosPardalos,editor,Advances<strong>in</strong>Optimization<strong>and</strong>Parallel Moscow,USSR,1988.<br />
[27]A.Kamath<strong>and</strong>N.Karmarkar,\Acont<strong>in</strong>uousapproachtocomputeupperbounds<strong>in</strong>quadratic maximizationproblemswith<strong>in</strong>tegerconstra<strong>in</strong>ts",<strong>in</strong>C.Floudas<strong>and</strong>P.Pardalos,editors, Comput<strong>in</strong>g.North-Holl<strong>and</strong>,1992.<br />
[28]A.Kamath<strong>and</strong>N.Karmarkar,\AnO(nL)iterationalgorithm<strong>for</strong>comput<strong>in</strong>gbounds<strong>in</strong> 1992. RecentAdvances<strong>in</strong>GlobalOptimization,pp.125{140.Pr<strong>in</strong>cetonUniversityPress,Ox<strong>for</strong>d,<br />
quadraticoptimizationproblems",<strong>in</strong>P.M.Pardalos,editor,Complexity<strong>in</strong>NumericalOpti-<br />
[30]E.D.Andersen,J.Gondzio,C.Meszaros,<strong>and</strong>X.Xu,\Implementationof<strong>in</strong>terior-po<strong>in</strong>t [29]S.J.Wright,Primal-DualInterior-Po<strong>in</strong>tMethods,SIAM,Philadelphia,1997. mization,pp.254{268.WorldScienticPublish<strong>in</strong>gCo.,S<strong>in</strong>gapore,1993.<br />
[31]M.Kojima,S.Mizuno,<strong>and</strong>A.Yoshise,\Aprimal-dual<strong>in</strong>teriorpo<strong>in</strong>tmethod<strong>for</strong>l<strong>in</strong>ear MathematicalProgramm<strong>in</strong>g,pp.189{252.Kluwer,1996. methods<strong>for</strong>largescalel<strong>in</strong>earprograms",<strong>in</strong>T.Terlaky,editor,InteriorPo<strong>in</strong>tMethodsof<br />
[32]M.Wright,\Interiormethods<strong>for</strong>constra<strong>in</strong>edoptimization",ActaNumerica,vol.1,pp. <strong>and</strong>RelatedMethods,pp.29{47.Spr<strong>in</strong>ger,1989. programm<strong>in</strong>g",<strong>in</strong>N.Megiddo,editor,Progress<strong>in</strong>MathematicalProgramm<strong>in</strong>g,Interior-Po<strong>in</strong>t<br />
[33]C.Helmberg,F.Rendl,R.J.V<strong>and</strong>erbei,<strong>and</strong>H.Wolkowicz,\An<strong>in</strong>terior-po<strong>in</strong>tmethod<strong>for</strong> semideniteprogramm<strong>in</strong>g",SIAMJ.onOptimization,vol.6,pp.342{361,1996. 341{407,1992.<br />
[34]M.Kojima,S.Sh<strong>in</strong>doh,<strong>and</strong>S.Hara,\Interior-po<strong>in</strong>tmethods<strong>for</strong>themonotonel<strong>in</strong>earcom-<br />
[35]R.D.C.Monteiro,\Primal-dualpathfollow<strong>in</strong>galgorithms<strong>for</strong>semideniteprogramm<strong>in</strong>g", Feb.1997. plementarityproblem<strong>in</strong>symmetricmatrices",SIAMJ.onOptimization,vol.7,pp.86{125,<br />
[36]F.Alizadeh,J.-P.A.Haeberly,<strong>and</strong>M.L.Overton,\Primal-dual<strong>in</strong>terior-po<strong>in</strong>tmethods <strong>for</strong>semideniteprogramm<strong>in</strong>g:convergencerates,stability<strong>and</strong>numericalresults",1996, SIAMJ.onMatrixAnalysis<strong>and</strong>Applications,1995,Toappear.<br />
[37]Yu.E.Nesterov<strong>and</strong>M.J.Todd,\Self-scaledcones<strong>and</strong><strong>in</strong>terior-po<strong>in</strong>tmethods<strong>for</strong>convex programm<strong>in</strong>g",MathematicsofOperationsResearch,vol.22,pp.1{42,1997. Manuscript.<br />
12