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Zbl 1041.90052
Ye, J.J.; Zhu, Qiji J.
Multiobjective optimization problem with variational inequality constraints. (English)
[J] Math. Program. 96, No.1 (A), 139-160 (2003). ISSN 0025-5610; ISSN 1436-4646/e

Summary: 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.

MSC 2000:: *90C29 Multi-objective programming, etc.
49J40 Variational methods including variational inequalities

Keywords: constraint qualification; preference; utility function; subdifferential calculus

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