Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0631.90077
Ferro, F.
A minimax theorem for vector-valued functions.
(English)
[J] J. Optimization Theory Appl. 60, No.1, 19-31 (1989). ISSN 0022-3239; ISSN 1573-2878/e

In this work, as usual in vector-valued optimization, we consider the partial ordering induced in a topological vector space by a closed and convex cone. In this way, we define maximal and minimal sets of a vector- valued function and consider minimax problems in this setting. Under suitable hypotheses (continuity, compactness, and special types of convexity), we prove that, for every $$\alpha \in Max\cup \sb{s\in X\sb 0}Min\sb wf(s,Y\sb 0),$$ there exists $$\beta \in Min\cup \sb{t\in Y\sb 0}Max f(X\sb 0,t)$$ such that $\beta\le \alpha$ (the exact meanings of the symbols are given in Section 2).
MSC 2000:
*90C31 Sensitivity, etc.

Keywords: vector-valued optimization; minimax problems

Highlights
Master Server