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Lower-Order Penalization Approach to Nonlinear Semidefinite Programming

  • X. X. Huang
  • X. Q.  Yang
  • K. L. Teo
Article

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.

Key Words

Semidefinite programming lower-order penalty methods Ekeland variational principle optimality conditions 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • X. X. Huang
    • 1
  • X. Q.  Yang
    • 2
  • K. L. Teo
    • 3
  1. 1.Department of Mathematics and Computer ScienceChongqing Normal University, Chongqing, China and School of Management, Fudan UniversityShanghaiChina
  2. 2.Department of Applied MathematicsHong Kong Polytechnic UniversityKowloonChina
  3. 3.Department of Mathematics and StatisticsCurtin University of TechnologyPerthAustralia

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