A sequential quadratic penalty method for nonlinear semidefinite programming

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)

Abstract

In this article, a nonlinear semidefinite program is reformulated into a mathematical program with a matrix equality constraint and a sequential quadratic penalty method is proposed to solve the latter problem. We discuss the differentiability and convexity of the penalty function. Necessary and sufficient conditions for the convergence of optimal values of penalty problems to that of the original semidefinite program are obtained. The convergence of optimal solutions of penalty problems to that of the original semidefinite program is also investigated. We show that any limit point of a sequence of stationary points of penalty problems satisfies the KKT optimality condition of the semidefinite program. Smoothed penalty problems that have the same order of smothness as the original semidefinite program are adopted. Corresponding results such as the convexity of the smoothed penalty function, the convergence of optimal values, optimal solutions and the stationary points of the smoothed penalty problems are obtained.
Original languageEnglish
Pages (from-to)715-738
Number of pages24
JournalOptimization
Volume52
Issue number6
DOIs
Publication statusPublished - 1 Dec 2003

Keywords

  • Convergence
  • Optimality condition
  • Penalty method
  • Semidefinite program
  • Smoothing method

ASJC Scopus subject areas

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

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