Skip to search formSkip to main content
You are currently offline. Some features of the site may not work correctly.

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… Expand
Wikipedia

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
Accelerated Regularized Newton Methods for Minimizing Composite Convex Functions
In this paper, we study accelerated Regularized Newton Methods for minimizing objectives formed as a sum of two functions: one is… Expand
Is this relevant?
2019
2019
A block symmetric Gauss–Seidel decomposition theorem for convex composite quadratic programming and its applications
For a symmetric positive semidefinite linear system of equations $$\mathcal{Q}{{\varvec{x}}}= {{\varvec{b}}}$$Qx=b, where… Expand
Is this relevant?
2018
2018
A proximal difference-of-convex algorithm with extrapolation
We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a… Expand
  • table 1
  • table 2
  • table 3
  • table 4
Is this relevant?
2017
2017
Further properties of the forward–backward envelope with applications to difference-of-convex programming
In this paper, we further study the forward–backward envelope first introduced in Patrinos and Bemporad (Proceedings of the IEEE… Expand
  • table 1
  • table 2
  • table 3
  • table 4
Is this relevant?
2017
2017
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… Expand
  • figure 4.1
  • figure 4.2
  • figure 4.3
  • figure 4.4
  • figure 4.5
Is this relevant?
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… Expand
Is this relevant?
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… Expand
Is this relevant?
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… Expand
Is this relevant?
Highly Cited
2005
Highly Cited
2005
Proximal Point Algorithm Controlled by a Slowly Vanishing Term: Applications to Hierarchical Minimization
Let $\Phi_0:\mathbb{R}^n\to \mathbb{R}\cup \{+\infty\}$ be a closed convex function and $\Phi_1:\mathbb{R}^n\to \mathbb{R}$ be a… Expand
Is this relevant?
1996
1996
An asymptotical variational principle associated with the steepest descent method for a convex function.
Let X be a real Hilbert space endowed with inner product 〈., .〉 and associated norm ‖.‖, and let f be a proper closed convex… Expand
Is this relevant?
By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy Policy, Terms of Service, and Dataset License
ACCEPT & CONTINUE