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Multiobjective optimization problem with variational inequality constraints


 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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Received: November 2000 / Accepted: October 2001 Published online: December 19, 2002

Key Words. Multiobjective optimization – Variational inequality – Complementarity constraint – Constraint qualification – Bilevel programming problem – Preference – Utility function – Subdifferential calculus – Variational principle

Research of this paper was supported by NSERC and a University of Victoria Internal Research Grant

Research was supported by the National Science Foundation under grants DMS-9704203 and DMS-0102496

Mathematics Subject Classification (2000): Sub49K24, 90C29

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Ye, J., Zhu, Q. Multiobjective optimization problem with variational inequality constraints. Math. Program., Ser. A 96, 139–160 (2003).

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  • Variational Inequality
  • Inequality Constraint
  • Constraint Qualification
  • Bilevel Programming
  • Multiobjective Optimization Problem