A generalization of a theorem of Arrow, Barankin and Blackwell to a nonconvex case
- Authors: Kasimbeyli, Nergiz , Kasimbeyli, Refail , Mammadov, Musa
- Date: 2016
- Type: Text , Journal article
- Relation: Optimization Vol. 65, no. 5 (May 2016), p. 937-945
- Full Text:
- Reviewed:
- Description: The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a partially ordered reflexive Banach space.
Farkas-type results for vector-valued functions with applications
- Authors: Dinh, Nguyen , Goberna, Miguel , López, Marco , Mo, T. H.
- Date: 2017
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 173, no. 2 (2017), p. 357-390
- Full Text:
- Reviewed:
- Description: The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space defined by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including multiobjective and scalar ones), vector variational inequalities, and vector equilibrium problems.