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Some convex programs without a duality gap. (English) Zbl 1176.90464

The author studies the convex programming problem:

v P =minf o (x)s.t.f i (x)0,i=1,...,m(P)

where each f i : n (-,) is a proper convex lower semicontinuous function and its associated dual:

v D =maxq(μ)whereq(μ)=inf x {f o (x)+ i=1 m f i (x)},μ0·(D)

The main result concerns the non-existence of the duality gap i.e. v P =v D . It is shown that for separable functions f o ,f 1 ,...,f m the relation v P =v D holds under the assumption of domf o 1=1 m domf i where domf={x|f(x)<}. The author gives also a sufficient condition involving weakly analytic functions.

90C25Convex programming
90C46Optimality conditions, duality
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