Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/19153
Title: Lower-order penalization approach to nonlinear semidefinite programming
Authors: Huang, XX
Yang, XQ 
Teo, KL
Keywords: Ekeland variational principle
Lower-order penalty methods
Optimality conditions
Semidefinite programming
Issue Date: 2007
Publisher: Springer
Source: Journal of optimization theory and applications, 2007, v. 132, no. 1, p. 1-20 How to cite?
Journal: Journal of optimization theory and applications 
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.
URI: http://hdl.handle.net/10397/19153
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-006-9055-2
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