On Chebyshev functions and Klee functions

DOI10.1016/j.jmaa.2010.03.041zbMath1211.49022OpenAlexW2013268819MaRDI QIDQ972484

Shawn Xianfu Wang

Publication date: 19 May 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.03.041

zbMATH Keywords

monotone operatorlimiting subdifferentialMoreau envelopeKlee envelopeChebyshev functionproximal mappingstrongly convex functionessentially strictly convex functionfarthest mappinghypoconvex functionKlee functionprox-bounded lower semicontinuous functionprox-regular function

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46) Nonsmooth analysis (49J52) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items (19)

A note on the Douglas-Rachford splitting method for optimization problems involving hypoconvex functions ⋮ On compositions of special cases of Lipschitz continuous operators ⋮ The NSLUC property and Klee envelope ⋮ Connectedness and other geometric properties of suns and Chebyshev sets ⋮ A Connection Between Red-Green Turing Machines and Watson-Crick T0L Systems ⋮ Dualities for Non-Euclidean Smoothness and Strong Convexity under the Light of Generalized Conjugacy ⋮ A continuous dynamical splitting method for solving ‘strongly+weakly’ convex programming problems ⋮ A Proximal Average for Prox-Bounded Functions ⋮ ENVELOPES FOR SETS AND FUNCTIONS: REGULARIZATION AND GENERALIZED CONJUGACY ⋮ On closures of preimages of metric projection mappings in Hilbert spaces ⋮ Attainment and (sub)differentiability of the supremal convolution of a function and square of the norm ⋮ The Moreau envelope function and proximal mapping in the sense of the Bregman distance ⋮ A characterization of essentially strictly convex functions on reflexive Banach spaces ⋮ Differential properties of the Moreau envelope ⋮ Generalized monotone operators and their averaged resolvents ⋮ Primal Lower Nice Functions and Their Moreau Envelopes ⋮ Bregman proximal mappings and Bregman-Moreau envelopes under relative prox-regularity ⋮ The attainment set of the $\varphi$-envelope and genericity properties ⋮ Convergence Analysis of Douglas--Rachford Splitting Method for “Strongly + Weakly” Convex Programming

Cites Work

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• Convexity of Chebyshev sets
• Autoconjugate representers for linear monotone operators
• Computing proximal points of nonconvex functions
• Bregman distances and Klee sets
• Bregman distances and Chebyshev sets
• Proximal mappings
• Duality for nonconvex optimization and its applications
• Prox-regular functions in Hilbert spaces
• Prox-regularity of functions and sets in Banach spaces
• Approximate mean value theorem for upper subderivatives
• Potpourri of Conjectures and Open Questions in Nonlinear Analysis and Optimization
• Monotone Operators and the Proximal Point Algorithm
• Variational Analysis
• Local differentiability of distance functions
• Prox-regular functions in variational analysis

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