Strongly convex functions, Moreau envelopes and the generic nature of convex functions with strong minimizers

Chayne Planiden; Xianfu Wang

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arXiv · 1507.07144

Strongly convex functions, Moreau envelopes and the generic nature of convex functions with strong minimizers

Chayne Planiden·Xianfu Wang

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Abstract

In this work, using Moreau envelopes, we define a complete metric for the set of proper lower semicontinuous convex functions. Under this metric, the convergence of each sequence of convex functions is epi-convergence. We show that the set of strongly convex functions is dense but it is only of the first category. On the other hand, it is shown that the set of convex functions with strong minima is of the second category.

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Chayne Planiden, Xianfu Wang. 2015-07-25. Strongly convex functions, Moreau envelopes and the generic nature of convex functions with strong minimizers. https://arxiv.org/abs/1507.07144

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