Invited Session Thu.1.H 1029

Thursday, 10:30 - 12:00 h, Room: H 1029

Cluster 15: Multi-objective optimization [...]

Vector optimization

 

Chair: César Gutiérrez and Vicente Novo

 

 

Thursday, 10:30 - 10:55 h, Room: H 1029, Talk 1

Maria Beatriz Hernández-Jiménez
Characterization of efficient solutions for non-regular multiobjective problemas with inequality-type constraints

Coauthors: Manuel Arana-Jiménez, Rafaela Osuna-Gómez, Gabriel Ruíz-Garzón

 

Abstract:
For multiobjective problems with inequality-type constraints the necessary conditions for efficient solutions are presented. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions, and they are based on the concept of 2-regularity introduced by Izmailov. In general, the necessary optimality conditions are not sufficient and the efficient solution set is not the same as the Karush-Kuhn-Tucker points set. So it is necessary to introduce generalized convexity notions. In the multiobjective nonregular case we give the notion of 2-KKT-pseudoinvex-II problems. This new concept of generalized convexity is both necessary and sufficient to guarantee the characterization of all efficient solutions based on the optimality conditions.

 

 

Thursday, 11:00 - 11:25 h, Room: H 1029, Talk 2

César Gutiérrez
Approximation of efficient sets via ε-efficient sets

Coauthors: Bienvenido Jiménez, Vicente Novo

 

Abstract:
When a vector optimization problem is solved, usually an approximate solution set is attained. In order to this surrogate optimization process works, the obtained ε-efficiency sets should satisfy certain continuity properties with respect to the solution set. In this talk we show several results from which one can analyze this problem, which are based on a generic ε-efficient concept. Finally, some of these results are applied to a vector optimization problem where the objective mapping is set-valued.

 

 

Thursday, 11:30 - 11:55 h, Room: H 1029, Talk 3

Fabián Flores-Bazán
Efficiency and ordering variational principles

 

Abstract:
It is shown that several results on ordering principles (among them the Brezis-Browder and the Ekeland variational ones on partially or quasi ordered spaces) that appear in the literature and have been proved in an independent way, have a common root: efficiency. Existence results of maximal elements for non constant binary relations are also discussed.

 

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