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Exact Penalization and Necessary Optimality Conditions for Multiobjective Optimization Problems with Equilibrium Constraints

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  • Shengkun Zhu
  • Shengjie Li

Abstract

A calmness condition for a general multiobjective optimization problem with equilibrium constraints is proposed. Some exact penalization properties for two classes of multiobjective penalty problems are established and shown to be equivalent to the calmness condition. Subsequently, a Mordukhovich stationary necessary optimality condition based on the exact penalization results is obtained. Moreover, some applications to a multiobjective optimization problem with complementarity constraints and a multiobjective optimization problem with weak vector variational inequality constraints are given.

Suggested Citation

  • Shengkun Zhu & Shengjie Li, 2014. "Exact Penalization and Necessary Optimality Conditions for Multiobjective Optimization Problems with Equilibrium Constraints," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:630547
    DOI: 10.1155/2014/630547
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    References listed on IDEAS

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    1. J. J. Ye & X. Y. Ye, 1997. "Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 977-997, November.
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