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Propagation of singularities of Moreau envelopes and distance functions in a Hilbert space
The Moreau envelopes of nonconvex functions on a real Hilbert space have points of nondifferentiability called singularities. For the first time in...
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Moreau–Yosida Regularization in DFT
Moreau–Yosida regularization is introduced into the framework of exact DFT. Moreau–Yosida regularization is a lossless operation on lower...
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Generalized Bregman Envelopes and Proximity Operators
Every maximally monotone operator can be associated with a family of convex functions, called the Fitzpatrick family or family of representative...
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Bregman Proximal Map**s and Bregman–Moreau Envelopes Under Relative Prox-Regularity
We systematically study the local single-valuedness of the Bregman proximal map** and local smoothness of the Bregman–Moreau envelope of a...
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Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs
Computing tasks may often be posed as optimization problems. The objective functions for real-world scenarios are often nonconvex and/or...
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Accelerated Proximal Envelopes: Application to Componentwise Methods
AbstractThis paper is devoted to a particular case of applying universal accelerated proximal methods for constructing computationally efficient...
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Proximal Map**s and Moreau Envelopes of Single-Variable Convex Piecewise Cubic Functions and Multivariable Gauge Functions
This work presents a collection of useful properties of the Moreau envelope for finite-dimensional, proper, lower semicontinuous, convex functions....
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The landscape of the proximal point method for nonconvex–nonconcave minimax optimization
Minimax optimization has become a central tool in machine learning with applications in robust optimization, reinforcement learning, GANs, etc. These...
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Convergence Rate of Proximal Inertial Algorithms Associated with Moreau Envelopes of Convex Functions
In a Hilbert space setting $${\mathcal...
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Coordinate descent methods beyond smoothness and separability
This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and...
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Compensated Convex-Based Transforms for Image Processing and Shape Interrogation
This paper reviews some recent applications of the theory of the compensated convex transforms or of the proximity hull as developed by the authors...
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Variational Convexity of Functions in Banach Spaces
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has...
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Mixed lattice structures and cone projections
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems,...
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Variable smoothing incremental aggregated gradient method for nonsmooth nonconvex regularized optimization
In this paper, we focus on the problem of minimizing the sum of nonconvex smooth component functions and a nonsmooth weakly convex function composed...
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Old and new challenges in Hadamard spaces
Hadamard spaces have traditionally played important roles in geometry and geometric group theory. More recently, they have additionally turned out to...