Contributiond to non-regular multiobjective optimization - Rahou Fatima Zahra (Université Sidi Mohamed Ben Abdellah, Faculté des Sciences - Dhar El Mahraz -, Fès, 2021)
In the framework of this thesis, we propose five works elaborated in the fields of multiobjective and set-valued optimization. Each work addresses the most important objective of optimization that is, characterizing a solution by necessary and sufficient conditions or both. The functions considred in all the works are neither convex nor differentiable. The first work of this thesis seeks to establish necessary and sufficient optimality conditions for a set valued optimization problem in terms of approximation under a generalized convexity. The second one investigates another set-valued optimization problem by giving necessary and sufficient optimality conditions in terms of directional convexificators, a new notion based on directions in which the considered function is continuous. The third one deals with an exact separation principle together with a special scalarization to derive the necessary optimality conditions for a multiobjective problem. The fourth work gives necessary optimality conditions for a fractional multiobjective optimization problem. Finally, Based upon the necessary optimality conditions established in the last work we provide sufficient and Mon-Weir duality results for the same fractional multiobjective optimization problem
"Contribution à l’optimisation multivoque non-régulière, Conditions d’optimalité et dualité"
Keywords: Mathématiques; Optimisation et recherche opérationnelle; Optimality conditions; Duality; Approximation; Convexificator