Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/14622
Title: A sequential quadratic penalty method for nonlinear semidefinite programming
Authors: Huang, XX
Yang, XQ 
Teo, KL
Keywords: Convergence
Optimality condition
Penalty method
Semidefinite program
Smoothing method
Issue Date: 2003
Publisher: Taylor & Francis
Source: Optimization, 2003, v. 52, no. 6, p. 715-738 How to cite?
Journal: Optimization 
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.
URI: http://hdl.handle.net/10397/14622
ISSN: 0233-1934
EISSN: 1029-4945
DOI: 10.1080/02331930310001637404
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