Displaying similar documents to “A note on essential components and essential weakly efficient solutions for multiobjective optimization problems.”

Weighted scalarization related to L p -metric and pareto optimality

Alexandra Šipošová (2008)

Kybernetika

Similarity:

Relations between (proper) Pareto optimality of solutions of multicriteria optimization problems and solutions of the minimization problems obtained by replacing the multiple criteria with L p -norm related functions (depending on the criteria, goals, and scaling factors) are investigated.

Optimality conditions for weak efficiency to vector optimization problems with composed convex functions

Radu Boţ, Ioan Hodrea, Gert Wanka (2008)

Open Mathematics

Similarity:

We consider a convex optimization problem with a vector valued function as objective function and convex cone inequality constraints. We suppose that each entry of the objective function is the composition of some convex functions. Our aim is to provide necessary and sufficient conditions for the weakly efficient solutions of this vector problem. Moreover, a multiobjective dual treatment is given and weak and strong duality assertions are proved.

Coercivity properties and well-posedness in vector optimization

Sien Deng (2003)

RAIRO - Operations Research - Recherche Opérationnelle

Similarity:

This paper studies the issue of well-posedness for vector optimization. It is shown that coercivity implies well-posedness without any convexity assumptions on problem data. For convex vector optimization problems, solution sets of such problems are non-convex in general, but they are highly structured. By exploring such structures carefully via convex analysis, we are able to obtain a number of positive results, including a criterion for well-posedness in terms of that of associated...