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Convex programs with an additional reverse convex constraint

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Abstract

A method is presented for solving a class of global optimization problems of the form (P): minimizef(x), subject toxD,g(x)≥0, whereD is a closed convex subset ofR n andf,g are convex finite functionsR n. Under suitable stability hypotheses, it is shown that a feasible point\(\bar x\) is optimal if and only if 0=max{g(x):xD,f(x)≤f(\(\bar x\))}. On the basis of this optimality criterion, the problem is reduced to a sequence of subproblemsQ k ,k=1, 2, ..., each of which consists in maximizing the convex functiong(x) over some polyhedronS k . The method is similar to the outer approximation method for maximizing a convex function over a compact convex set.

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Communicated by A. V. Fiacco

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Tuy, H. Convex programs with an additional reverse convex constraint. J Optim Theory Appl 52, 463–486 (1987). https://doi.org/10.1007/BF00938217

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