In this note, a general cone separation theorem between two subsets of image space is presented. With the aid of this, optimality conditions and duality for vector optimization of set-valued functions in locally convex spaces are discussed.
Conjugate Duality in Set-Valued Vector Optimization
β Scribed by Wen Song
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 236 KB
- Volume
- 216
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, conjugate duality results for convexlike set-valued vector optimization problems are presented under closedness or boundedness hypotheses. Some properties of the value mapping of a set-valued vector optimization problem are studied. A conjugate duality result is also proved for a convex set-valued vector optimization problem without the requirements of closedness and boundedness.
π SIMILAR VOLUMES
This paper establishes an alternative theorem for generalized inequality-equality Ε½ . systems of set-valued maps. Based on this, several Lagrange multiplier type as well as saddle point type necessary and sufficient conditions are obtained for the existence of weak minimizers in vector optimization
A closed nonvoid subset Z of a Banach space X is called antiproximinal if no point outside Z has a nearest point in Z. The aim of the present paper is to prove that, for a compact Hausdorff space T and a real Banach space E, the Banach space C T E , of all continuous functions defined on T and with