Necessary Optimality Conditions and a New Approach to Multiobjective Bilevel Optimization Problems |
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Authors: | N Gadhi S Dempe |
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Institution: | 1.Department of Mathematics, Dhar El Mahraz,Sidi Mohamed Ben Abdellah University,Fes,Morocco;2.Department of Mathematics and Computers Sciences,Technical University Bergakademie Freiberg,Freiberg,Germany |
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Abstract: | Multiobjective optimization problems typically have conflicting objectives, and a gain in one objective very often is an expense
in another. Using the concept of Pareto optimality, we investigate a multiobjective bilevel optimization problem (say, P). Our approach consists of proving that P is locally equivalent to a single level optimization problem, where the nonsmooth Mangasarian–Fromovitz constraint qualification
may hold at any feasible solution. With the help of a special scalarization function introduced in optimization by Hiriart–Urruty,
we convert our single level optimization problem into another problem and give necessary optimality conditions for the initial
multiobjective bilevel optimization problem P. |
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