set-valued optimization problem – Optimization Online

Some criteria for error bounds in set optimization

Published: 2012/08/03, Updated: 2012/08/29

Multi-Criteria Optimization, Nonsmooth Optimization coderivative, constraint set, error bound, henig efficient solution, metric subregularity, pareto efficient solution, set-valued optimization problem, solution set, subdifferential, super efficient solution

We obtain sufficient and/or necessary conditions for global/local error bounds for the distances to some sets appeared in set optimization studied with both the set approach and vector approach (sublevel sets, constraint sets, sets of {\it all } Pareto efficient/ Henig proper efficient/super efficient solutions, sets of solutions {\it corresponding to one} Pareto efficient/Henig proper … Read more

Optimality conditions for various efficient solutions involving coderivatives: from set-valued optimization problems to set-valued equilibrium problems

Published: 2010/08/02, Updated: 2017/04/24

Xuan Duc Ha Truong

Complementarity and Variational Inequalities, Multi-Criteria Optimization, Nonsmooth Optimization coderivative, necessary optimality conditions, normal cone, pareto efficient solutions, properly efficient solutions, quasi weakly efficient solutions, relative efficient solutions, set-valued equilibrium problem, set-valued optimization problem, strongly efficient solutions, sufficient optimality conditions, vector equilibrium problem, vector variational inequality, weakly efficient solutions

We present a new approach to the study of a set-valued equilibrium problem (for short, SEP) through the study of a set-valued optimization problem with a geometric constraint (for short, SOP) based on an equivalence between solutions of these problems. As illustrations, we adapt to SEP enhanced notions of relative Pareto efficient solutions introduced in … Read more