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Proximal mappings and moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions

Chapter


Abstract


  • This work presents a collection of useful properties of the Moreau envelope for finite-dimensional, proper, lower semicontinuous, convex functions. In particular, gauge functions and piecewise cubic functions are investigated and their Moreau envelopes categorized. Characterizations of convex Moreau envelopes are established; topics include strict convexity, strong convexity, and Lipschitz continuity.

Publication Date


  • 2019

Citation


  • Planiden, C. & Wang, X. (2019). Proximal mappings and moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions. In S. Hosseini, B. S. Mordukhovich & A. Uschmajew (Eds.), Nonsmooth Optimization and Its Applications (pp. 89-130). Switzerland: Springer Nature.

International Standard Book Number (isbn) 13


  • 9783030113698

Scopus Eid


  • 2-s2.0-85064656069

Book Title


  • Nonsmooth Optimization and Its Applications

Start Page


  • 89

End Page


  • 130

Place Of Publication


  • Switzerland

Abstract


  • This work presents a collection of useful properties of the Moreau envelope for finite-dimensional, proper, lower semicontinuous, convex functions. In particular, gauge functions and piecewise cubic functions are investigated and their Moreau envelopes categorized. Characterizations of convex Moreau envelopes are established; topics include strict convexity, strong convexity, and Lipschitz continuity.

Publication Date


  • 2019

Citation


  • Planiden, C. & Wang, X. (2019). Proximal mappings and moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions. In S. Hosseini, B. S. Mordukhovich & A. Uschmajew (Eds.), Nonsmooth Optimization and Its Applications (pp. 89-130). Switzerland: Springer Nature.

International Standard Book Number (isbn) 13


  • 9783030113698

Scopus Eid


  • 2-s2.0-85064656069

Book Title


  • Nonsmooth Optimization and Its Applications

Start Page


  • 89

End Page


  • 130

Place Of Publication


  • Switzerland