Strong duality for infinite-dimensional vector-valued programming problems

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).