subgradient matlab,Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones-英文文献.pd...

Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones-英文文献

Using SeDuMi a MATLAB to olb ox for optimization over

symmetric cones

Jos F Sturm

Communications Research Lab oratory McMaster University Hamilton Canada

Supp orted by Netherlands Organization for Scientic Research NWO

Email sturmcauchycrlmcmasterca

August

Abstract

SeDuMi is an addon for MATLAB that lets you solve optimization problems with linear

quadratic and semideniteness constraints It is p ossible to have complex valued data and

variables in SeDuMi Moreover large scale optimization problems are solved eciently by

exploiting sparsity This pap er describ es how to work with this to olb ox

KEY W ORDS Symmetric cone semidenite programming second order cone program

ming selfduality MATLAB SeDuMi

SeDuMi stands for SelfDualMinimization it implements the selfdual emb edding technique

for optimization over selfdual homogeneous cones The selfdual emb edding technique as pro

p osed Ye To dd and Mizuno essentially makes it p ossible to solve certain optimization

problems in a single phase leading either to an optimal solution or a certicate of infeasibility

Optimization over selfdual homogeneous cones or more concisely optimization over symmetric

cones was rst studied by Nesterov and To dd and is currently an active area of research

Semidenite programming is a sp ecial case of optimization over symmetric cones The p op

ular package SP by Vandenb erghe and Boyd is one of the rst software to ols that was de

velop ed for semidenite programming Some control theorists use SP indirectly via LMITOOL

by El Ghaoui Nikoukhah and Deleb ecque or MRCT by Dus