Minimax Theory and its Applications 07 (2022), No. 1, 131--158
Copyright Heldermann Verlag 2022
Sequential Pareto Subdifferential Multi-Composition Rule and Application to Multiobjective Minimax Location Problems
Issam Dali
Dept. of Mathematics, Faculty of Sciences, El-Jadida, Morocco
dali.issam@gmail.com
Mohamed Laghdir
Dept. of Mathematics, Faculty of Sciences, El-Jadida, Morocco
laghdirm@gmail.com
Mohamed B. Moustaid
Dept. of Mathematics, Faculty of Sciences, El-Jadida, Morocco
bilalmoh39@gmail.com
In the absence of any qualification condition, we provide a sequential formula for the weak/proper Pareto subdifferential of multi-composed convex vector mappings. For illustrating this formula, we propose deriving sequential optimality conditions characterizing weakly/properly efficient solutions of multiobjective minimax location problems with infimal distances. We present an example of multiobjective bilevel programming problems with an extremal value function, where the standard Lagrange multipliers conditions can not be derived due to the lack of constraint qualification and the sequential conditions hold.
Keywords: Sequential Pareto subdifferential, multi-composed vector mappings, sequential weak efficiency, sequential proper efficiency, multiobjective minimax location problems, multiobjective bilevel programming problems.
MSC: 49K35, 90C25, 90C29, 90C47, 90C48.
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