Necessary Optimality Conditions and a New Approach to Multiobjective Bilevel Optimization Problems

N. Gadhi () and S. Dempe ()
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N. Gadhi: Sidi Mohamed Ben Abdellah University
S. Dempe: Technical University Bergakademie Freiberg

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 1, No 5, 100-114

Abstract: 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.

Keywords: Multiobjective optimization; Local weak efficient solution; Optimality conditions; Optimal value function; Bilevel programming (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-012-0046-1

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