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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Communicated by M. Avriel
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Aze, D., Volle, M. A stability result in quasi-convex programming. J Optim Theory Appl 67, 175–184 (1990). https://doi.org/10.1007/BF00939742
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DOI: https://doi.org/10.1007/BF00939742