ISSN:
1573-2878
Keywords:
Cone concavity
;
strong maximal points
;
dual problems
;
strong saddlepoints
;
pseudotangent cones
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetX,Y andZ be locally convex real topological vector spaces,A⊂X a convex subset, and letC⊂Y,E⊂Z be cones. Letf:X→Z beE-concave andg:X→Y beC-concave functions. We consider a concave programming problem with respect to an abstract cone and its strong dual problem as follows: $$\begin{gathered} (P)maximize f(x), subject to x \in A, g(x) \in C, \hfill \\ (SD)minimize \left\{ {\mathop \cup \limits_{\varphi \in C^ + } \max \{ (f + \varphi \circ g)(A):E\} } \right\}, \hfill \\ \end{gathered} $$ , whereC + denotes the set of all nonnegative continuous linear operators fromY toZ and (SD) is the strong dual problem to (P). In this paper, the authors find a necessary condition of strong saddle point for Problem (P) and establish the strong duality relationships between Problems (P) and (SD).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00939816
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