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Optimality conditions in set-valued optimization using approximations as generalized derivatives

Gadhi Nazih Abderrazzak, Ichatouhane Aissam

Control and Cybernetics

2022

Vol. 51, No. 4

425--444

The set criterion is an appropriate defining approach regarding the solutions for the set-valued optimization problems. By using approximations as generalized derivatives of set-valued mappings, we establish necessary optimality conditions for a constrained set-valued optimization problem in the sense of set optimization in terms of asymptotical pointwise compact approximations. Sufficient optimality conditions are then obtained through first-order strong approximations of data set-valued mappings.

Necessary optimality conditions for robust nonsmooth multiobjective optimization problems

Gadhi Nazih Abderrazzak, Ohda Mohamed

Control and Cybernetics

2022

Vol. 51, No. 3

289--302

This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly robust efficient solutions of the considered problem. These optimality conditions are presented in terms of Karush-Kuhn-Tucker multipliers and convexificators of the related functions. Examples illustrating our findings are also given.

Optimality conditions for a set-valued optimization problem in terms of approximations

Gadhi Nazih Abderrazzak, Rahou Fatima Zahra, El Idrissi Mohammed

Control and Cybernetics

2019

Vol. 48, No. 3

439--452

In this paper, we are concerned with a constrained set-valued optimization problem (P). Using support functions, we give necessary optimality conditions in terms of Karush-Kuhn-Tucker (KKT) multipliers and approximations. Under generalized convex- ity, we investigate sufficient optimality conditions. An example illustrating our findings is also given.