Strongly Convex Functions, Moreau Envelopes, and the Generic Nature of Convex Functions with Strong Minimizers

DOI10.1137/15M1035550zbMath1347.49023arXiv1507.07144OpenAlexW2240332484MaRDI QIDQ2816239

Chayne Planiden, Shawn Xianfu Wang

Publication date: 4 July 2016

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.07144

zbMATH Keywords

lower semicontinuitycomplete metric spaceepi-convergenceBaire categorystrongly convex functionsmeager setproximal mappingMoreau envelopesepi-topologygeneric setAttouch-Wets metricstrong minimizers

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Nonsmooth analysis (49J52) Baire category, Baire spaces (54E52) Convex functions and convex programs in convex geometry (52A41) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories in calculus of variations and optimal control (49J99)

Related Items (9)

Epi-convergence: the Moreau envelope and generalized linear-quadratic functions ⋮ A linear-time algorithm to compute the conjugate of convex piecewise linear-quadratic bivariate functions ⋮ A Variable Sample-Size Stochastic Quasi-Newton Method for Smooth and Nonsmooth Stochastic Convex Optimization ⋮ The Bregman Proximal Average ⋮ An adaptive sampling augmented Lagrangian method for stochastic optimization with deterministic constraints ⋮ A Proximal Average for Prox-Bounded Functions ⋮ Unnamed Item ⋮ Conditions for the existence, identification and calculus rules of the threshold of prox-boundedness ⋮ Smoothed Variable Sample-Size Accelerated Proximal Methods for Nonsmooth Stochastic Convex Programs

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