Multiobjective optimization problem with variational inequality constraints |
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Authors: | JJ Ye Qiji J Zhu |
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Institution: | (1) Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada V8W 3P4; e-mail: janeye@math.uvic.ca, CA;(2) Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA; e-mail: zhu@math-stat.wmich.edu, US |
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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.
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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