RIS ID

121656

Publication Details

Planiden, C. & Wang, X. (2018). Epi-convergence: the Moreau envelope and generalized linear-quadratic functions. Journal of Optimization Theory and Applications, 177 (1), 21-63.

Abstract

This work explores the class of generalized linear-quadratic functions, constructed using maximally monotone symmetric linear relations. Calculus rules and properties of the Moreau envelope for this class of functions are developed. In finite dimensions, on a metric space defined by Moreau envelopes , we consider the epigraphical limit of a sequence of quadratic functions and categorize the results. We examine the question of when a quadratic function is a Moreau envelope of a generalized linear-quadratic function; characterizations involving nonexpansiveness and Lipschitz continuity are established. This work generalizes some results by Hiriart-Urruty and by Rockafellar and Wets.

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Link to publisher version (DOI)

http://dx.doi.org/10.1007/s10957-018-1254-0