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Two theoretical results for sequential semidefinite programming

Rodrigo GarcÚs (wgomez***at***ufro.cl)
Walter Gomez Bofill (wgomez***at***ufro.cl)
Florian Jarre (jarre***at***opt.uni-duesseldorf.de)

Abstract: We examine the local convergence of a sequential semidefinite programming approach for solving nonlinear programs with nonlinear semidefiniteness constraints. Known convergence results are extended to slightly weaker second order sufficient conditions and the resulting subproblems are shown to have local convexity properties that imply a weak form of self-concordance of the barrier subproblems.

Keywords: semidefinite programming, second order sufficient condition, sequential quadratic programming, quadratic semidefinite program, self-concordance, sensitivity, convergence.

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Linear, Cone and Semidefinite Programming (Other )

Category 3: Optimization Software and Modeling Systems (Other )

Citation: Preprint, Mathematisches Institut, Universitaet Duesseldorf, Nov. 2007.

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Entry Submitted: 11/01/2007
Entry Accepted: 11/01/2007
Entry Last Modified: 02/01/2008

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