The Proximal Average: Basic Theory
From MaRDI portal
Publication:3629518
DOI10.1137/070687542zbMath1172.26003OpenAlexW1973823738WikidataQ56446093 ScholiaQ56446093MaRDI QIDQ3629518
Rafal Goebel, Heinz H. Bauschke, Yves Lucet, Shawn Xianfu Wang
Publication date: 27 May 2009
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/070687542
convex functionsubdifferentialconvex analysisMoreau envelopeFenchel conjugateproximal averageproximal mappingepi-continuity
Related Items
Nonsmoothness in machine learning: specific structure, proximal identification, and applications ⋮ Self-Dual Smooth Approximations of Convex Functions via the Proximal Average ⋮ Graph-Matrix Calculus for Computational Convex Analysis ⋮ Convergence results for a self-dual regularization of convex problems ⋮ Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Theoretical Foundations ⋮ Autoconjugate representers for linear monotone operators ⋮ Near equality, near convexity, sums of maximally monotone operators, and averages of firmly nonexpansive mappings ⋮ Computing the conjugate of convex piecewise linear-quadratic bivariate functions ⋮ Proximal average approximated incremental gradient descent for composite penalty regularized empirical risk minimization ⋮ The Bregman Proximal Average ⋮ Three step algorithm for weighted resolvent average of a finite family of monotone operators ⋮ Unnamed Item ⋮ The resolvent average on symmetric cones ⋮ Contractive barycentric maps and \(L^{1}\) ergodic theorems on the cone of positive definite matrices ⋮ Convex hull algorithms for piecewise linear-quadratic functions in computational convex analysis ⋮ A geometric mean of parameterized arithmetic and harmonic means of convex functions ⋮ A Proximal Average for Prox-Bounded Functions ⋮ Resolvent and proximal compositions ⋮ Convexity of the proximal average ⋮ Maximal monotone operators and the proximal point algorithm in the presence of computational errors ⋮ Strong Convergence Theorems for Weighted Resolvent Average of a Finite Family of Monotone Operators ⋮ A proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in the presence of computational errors ⋮ The NC-proximal average for multiple functions ⋮ The optimal value and optimal solutions of the proximal average of convex functions ⋮ Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions ⋮ Nonexpansiveness of the resolvent average ⋮ The resolvent average on symmetric cones of JB-algebras ⋮ Efficient Learning with a Family of Nonconvex Regularizers by Redistributing Nonconvexity ⋮ Structure preserving matrix means on the Marcus-Minc stochastic matrices ⋮ Compositions and averages of two resolvents: relative geometry of fixed points sets and a partial answer to a question by C.\,Byrne ⋮ The matrix geometric mean of parameterized, weighted arithmetic and harmonic means ⋮ Techniques and Open Questions in Computational Convex Analysis ⋮ The resolvent average for positive semidefinite matrices ⋮ On convex envelopes and regularization of non-convex functionals without moving global minima ⋮ The Resolvent Average of Monotone Operators: Dominant and Recessive Properties ⋮ On the asymptotic behaviour of the Aragón Artacho-Campoy algorithm ⋮ Inexact stochastic subgradient projection method for stochastic equilibrium problems with nonmonotone bifunctions: application to expected risk minimization in machine learning ⋮ Strongly Convex Functions, Moreau Envelopes, and the Generic Nature of Convex Functions with Strong Minimizers ⋮ The kernel average for two convex functions and its application to the extension and representation of monotone operators ⋮ Inexact proximal point methods in metric spaces ⋮ Computation of the epsilon-subdifferential of convex piecewise linear-quadratic functions in optimal worst-case time ⋮ Unnamed Item
