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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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Convex analysis
Convex conjugateConvex functionEpigraph (mathematics)Proper convex function

Papers overview

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2015
2015
Accelerated Mirror Descent In Continuous and Discrete Time Supplementary material , NIPS 2015
1 Mirror operator ∇ψ * In this section, we discuss properties of distance generating functions and their subdif-ferentials. Let… 
2013
2013
An Algorithm Using Moreau-Yosida Regularization for Minimization of a Nondifferentiable Convex Function
In this paper we present an algorithm for minimization of a nondifferentiable proper closed convex function. Using the second… 
2012
2012
Nondifferentiable Convex Optimization : An Algorithm Using Moreau-Yosida Regularization
In this paper we present an algorithm for minimization of a nondifferentiable proper closed convex function. Using the second… 
2011
2011
CLOSED MEANS CONTINUOUS IFF POLYHEDRAL: A CONVERSE OF THE GKR THEOREM
Given x, a point of a convex subset C of an Euclidean space, the two following statements are proven to be equivalent: (i) any… 
1998
1998
Generalized Bundle Methods * Antonio Frangioni †
We study a class of generalized bundle methods for which the stabilizing term can be any closed convex function satisfying…