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

Journal Article


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.

Publication Date


  • 2016

Geographic Focus


Citation


  • 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.

Scopus Eid


  • 2-s2.0-84976878450

Number Of Pages


  • 23

Start Page


  • 1341

End Page


  • 1364

Volume


  • 26

Issue


  • 2

Place Of Publication


  • United States

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.

Publication Date


  • 2016

Geographic Focus


Citation


  • 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.

Scopus Eid


  • 2-s2.0-84976878450

Number Of Pages


  • 23

Start Page


  • 1341

End Page


  • 1364

Volume


  • 26

Issue


  • 2

Place Of Publication


  • United States