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Closed convex function

In mathematics, a function is said to be closed if for each , the sublevel set is a closed set. Equivalently, if the epigraph defined by is closed… 
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Related topics

Related topics

5 relations

Broader (1)

Convex analysis
Convex conjugateConvex functionEpigraph (mathematics)Proper convex function

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2019
2019
Potential-based analyses of first-order methods for constrained and composite optimization
We propose potential-based analyses for first-order algorithms applied to constrained and composite minimization problems. We… 
2018
2018
A refined convergence analysis of pDCAe\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs…
We consider the problem of minimizing a difference-of-convex (DC) function, which can be written as the sum of a smooth convex… 
2017
2017
Adaptive Proximal Average Approximation for Composite Convex Minimization
We propose a fast first-order method to solve multi-term nonsmooth composite convex minimization problems by employing a… 
2017
2017
A block symmetric Gauss–Seidel decomposition theorem for convex composite quadratic programming and its applications
For a symmetric positive semidefinite linear system of equations Qx=b\documentclass[12pt]{minimal} \usepackage{amsmath… 
Highly Cited
2015
Highly Cited
2015
Linear Convergence of Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems
In this paper, we study the proximal gradient algorithm with extrapolation for minimizing the sum of a Lipschitz differentiable… 
Highly Cited
2014
Highly Cited
2014
Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures
In this paper we study distributionally robust constraints on risk measures (such as standard deviation less the mean… 
2013
2013
A converse of the Gale-Klee-Rockafellar theorem: Continuity of convex functions at the boundary of their domains
Given x0, a point of a convex subset C of a Euclidean space, the two following statements are proven to be equivalent: (i) every… 
Review
2009
Review
2009
What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications
Computational convex analysis algorithms have been rediscovered several times in the past by researchers from different fields… 
2005
2005
Convergence of a Hybrid Projection-Proximal Point Algorithm Coupled with Approximation Methods in Convex Optimization
In order to minimize a closed convex function that is approximated by a sequence of better behaved functions, we investigate the… 
Highly Cited
2002
Highly Cited
2002
Generalized Bundle Methods
We study a class of generalized bundle methods for which the stabilizing term can be any closed convex function satisfying… 
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