ZERO DUALITY GAPS IN INFINITE-DIMENSIONAL PROGRAMMING

In this paper we study the following infinite-dimensional programming problem: (P) μ{colon equals}inf f0(x), subject to x∈C, fi(x)≤0, i∈I, where I is an index set with possibly infinite cardinality and C is an infinite-dimensional set. Zero duality gap results are presented under suitable regularity hypotheses for convex-like (nonconvex) and convex infinitely constrained program (P). Various properties of the value function of the convex-like program and its connections to the regularity hypotheses are studied. Relationships between the zero duality gap property, semicontinuity, and ε-subdifferentiability of the value function are examined. In particular, a characterization for a zero duality gap is given, using the ε-subdifferential of the value function without convexity. © 1990 Plenum Publishing Corporation.