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Epi-convergence: the Moreau envelope and generalized linear-quadratic functions

Journal Article


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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.

Publication Date


  • 2018

Citation


  • 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.

Scopus Eid


  • 2-s2.0-85045059156

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2139&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/1137

Number Of Pages


  • 42

Start Page


  • 21

End Page


  • 63

Volume


  • 177

Issue


  • 1

Place Of Publication


  • United States

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.

Publication Date


  • 2018

Citation


  • 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.

Scopus Eid


  • 2-s2.0-85045059156

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2139&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/1137

Number Of Pages


  • 42

Start Page


  • 21

End Page


  • 63

Volume


  • 177

Issue


  • 1

Place Of Publication


  • United States