Mathematical Programming

, Volume 96, Issue 1, pp 139–160 | Cite as

Multiobjective optimization problem with variational inequality constraints

  • J.J. Ye
  • Qiji J. Zhu

Abstract.

 We study a general multiobjective optimization problem with variational inequality, equality, inequality and abstract constraints. Fritz John type necessary optimality conditions involving Mordukhovich coderivatives are derived. They lead to Kuhn-Tucker type necessary optimality conditions under additional constraint qualifications including the calmness condition, the error bound constraint qualification, the no nonzero abnormal multiplier constraint qualification, the generalized Mangasarian-Fromovitz constraint qualification, the strong regularity constraint qualification and the linear constraint qualification. We then apply these results to the multiobjective optimization problem with complementarity constraints and the multiobjective bilevel programming problem.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • J.J. Ye
    • 1
  • Qiji J. Zhu
    • 2
  1. 1.Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada V8W 3P4; e-mail: janeye@math.uvic.caCA
  2. 2.Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA; e-mail: zhu@math-stat.wmich.eduUS

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