A sequential quadratic penalty method for nonlinear semidefinite programming

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 suf...

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Veröffentlicht in:Optimization Jg. 52; H. 6; S. 715 - 738
Hauptverfasser: Huang, X.X., Yang, X.Q., Teo, K.L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Taylor & Francis Group 01.12.2003
Schlagworte:
Convergence
Mathematics Subject Classifications 2000: 90C22
Optimality condition
Penalty method
Semidefinite program
Smoothing method
ISSN:0233-1934, 1029-4945
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Zusammenfassung: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.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331930310001637404