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Zero duality gaps in infinite-dimensional programming. (English) Zbl 0687.90077

We study the following infinite-dimensional programming problem

(P)μ:=inff 0 (x),subjecttoxC,f i (x),iI,

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 programs (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 the value function without convexity is given, using the ϵ-subdifferential of the value function.

Reviewer: V.Jeyakumar
MSC:
90C30Nonlinear programming
90C34Semi-infinite programming
49N15Duality theory (optimization)
90C48Programming in abstract spaces
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