Lower-order penalization approach to nonlinear semidefinite programming

X. X. Huang, Xiaoqi Yang, K. L. Teo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

Abstract

In this paper, we reformulate a nonlinear semidefinite programming problem into an optimization problem with a matrix equality constraint. We apply a lower-order penalization approach to the reformulated problem. Necessary and sufficient conditions that guarantee the global (local) exactness of the lower-order penalty functions are derived. Convergence results of the optimal values and optimal solutions of the penalty problems to those of the original semidefinite program are established. Since the penalty functions may not be smooth or even locally Lipschitz, we invoke the Ekeland variational principle to derive necessary optimality conditions for the penalty problems. Under certain conditions, we show that any limit point of a sequence of stationary points of the penalty problems is a KKT stationary point of the original semidefinite program.
Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalJournal of Optimization Theory and Applications
Volume132
Issue number1
DOIs
Publication statusPublished - 1 Jan 2007

Keywords

  • Ekeland variational principle
  • Lower-order penalty methods
  • Optimality conditions
  • Semidefinite programming

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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