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

By Chayne Planiden and Xianfu Wang

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 epiconvergence. 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

Topics: Engineering, Science and Technology Studies
Publisher: 'Sociological Research Online'
Year: 2016
DOI identifier: 10.1137/15m1035550
OAI identifier: oai:ro.uow.edu.au:eispapers1-2345
Provided by: Research Online
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