Optimality conditions and duality in terms of convexificators for multiobjective bilevel programming problem with equilibrium constraints

This paper is devoted to the investigation of a nonsmooth multiobjective bilevel programming problem with equilibrium constraints (( MBPP ) for short) in terms of convexificators in finite-dimensional spaces. We present necessary optimality conditions for the local weak efficient solution to such pr...

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Bibliographic Details
Published in:Computational & applied mathematics 2021-03, Vol.40 (2), Article 37
Main Authors: Van Su, Tran, Hang, Dinh Dieu, Dieu, Nguyen Cong
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Convexity
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
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Summary:This paper is devoted to the investigation of a nonsmooth multiobjective bilevel programming problem with equilibrium constraints (( MBPP ) for short) in terms of convexificators in finite-dimensional spaces. We present necessary optimality conditions for the local weak efficient solution to such problem. Under the Mangasarian–Fromovitz and generalized standard Abadie type constraint qualification in the sense of convexificators, we establish as an application the Wolfe and Mond-Weir type dual problem for the problem ( MBPP ). Besides, we provide strong and weak duality theorems for the original problem and its Wolfe and Mond–Weir type dual problem under suitable assumptions on the ∂ ∗ -convexity and the upper semi-regularity of objective and constraint functions. Illustrative examples are also proposed to demonstrate the main results of the paper.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-021-01431-8