A stability result in quasi-convex programming |
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Authors: | D Aze M Volle |
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Institution: | (1) Department of Mathematics, University of Perpignan, Perpignan, France;(2) Department of Mathematics, University of Avignon, Avignon, France |
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Abstract: | Combining a result on the lower semicontinuity of the intersection of two convex-valued multifunctions and the level set approach of epi-convergence, we obtain results on the epi-upper semicontinuity of the supremum and the sum of two families of quasi-convex functions. As a consequence, we give some condition ensuring the stability of a quasi-convex program under a perturbation of the objective functions and the constraint sets. |
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Keywords: | Convexity quasi-convexity set convergence epi-semicontinuity epi-convergence value functions |
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