Necessary conditions in multiobjective optimization with equilibrium constraints

We study multiobjective optimization problems with equilibrium constraints (MOPECs) described by parametric generalized equations in the form 0 G(x, y) + Q(x, y), where both mappings G and Q are set-valued. Such models arise particularly from certain optimization-related problems governed by variati...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2007-11, Vol.135 (2), p.179-203
Main Authors: BAO, T. Q, GUPTA, P, MORDUKHOVICH, B. S
Format: Article
Language:English
Subjects:
Applied sciences
Banach spaces
Bibliographic literature
Calculus of variations and optimal control
Computer programming
Differentiation
Equilibrium
Exact sciences and technology
Inequalities
Inequality
Mapping
Mathematical analysis
Mathematical functions
Mathematical models
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Optimization
Programming
Sciences and techniques of general use
Specifications
Studies
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Summary:We study multiobjective optimization problems with equilibrium constraints (MOPECs) described by parametric generalized equations in the form 0 G(x, y) + Q(x, y), where both mappings G and Q are set-valued. Such models arise particularly from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish verifiable necessary conditions for the general problems under consideration and for their important specifications by using modern tools of variational analysis and generalized differentiation. The application of the obtained necessary optimality conditions is illustrated by a numerical example from bilevel programming with convex while nondifferentiable data. [PUBLICATION ABSTRACT]
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-007-9209-x