Abstract
In this paper we study the following infinite-dimensional programming problem: (P) μ≔inff0(x), subject tox∈C,fi(x)≤0,i∈I, whereI is an index set with possibly infinite cardinality andC 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 e-subdifferentiability of the value function are examined. In particular, a characterization for a zero duality gap is given, using the e-subdifferential of the value function without convexity.
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