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

Authors

Chayne Planiden, University of British Columbia, OkanaganFollow
Xianfu Wang, University of British Columbia, OkanaganFollow

RIS ID

121658

Publication Details

Planiden, C. & Wang, X. (2016). Strongly convex functions, Moreau envelopes and the generic nature of convex functions with strong minimizers. SIAM Journal on Optimization, 26 (2), 1341-1364.

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.