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Zbl 0687.90077
Jeyakumar, V.; Wolkowicz, H.
Zero duality gaps in infinite-dimensional programming.
(English)
[J] J. Optimization Theory Appl. 67, No.1, 87-107 (1990). ISSN 0022-3239; ISSN 1573-2878/e

We study the following infinite-dimensional programming problem $$(P)\quad \mu:=\inf f\sb 0(x),\quad subject\quad to\quad x\in C,\quad f\sb i(x)\le,\quad i\in I,$$ 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 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 $\epsilon$- subdifferentiability of the value function are examined. In particular, a characterization for the value function without convexity is given, using the $\epsilon$-subdifferential of the value function.
[V.Jeyakumar]
MSC 2000:
*90C30 Nonlinear programming
90C34 Semi-infinite programming
49N15 Duality theory (optimization)
90C48 Programming in abstract spaces

Keywords: infinite-dimensional programming; duality gap; convex infinitely constrained programs; semicontinuity; epsilon-subdifferentiability; value function

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