Lower-Order Penalization Approach to Nonlinear Semidefinite Programming

X. X. Huang, X. Q. Yang and K. L. Teo
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X. X. Huang: Chongqing Normal University, Chongqing, China and School of Management, Fudan University
X. Q. Yang: Hong Kong Polytechnic University
K. L. Teo: Curtin University of Technology

Journal of Optimization Theory and Applications, 2007, vol. 132, issue 1, No 1, 20 pages

Abstract: 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.

Keywords: Semidefinite programming; lower-order penalty methods; Ekeland variational principle; optimality conditions (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-006-9055-2

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