A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces

Authors:
Heinz H. Bauschke;Patrick L. Combettes
Affiliations:
-;-
Venue:
Mathematics of Operations Research
Year:
2001

Citing 0
Cited 28

Some recent advances in projection-type methods for variational inequalities

Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Finding the projection of a point onto the intersection of convex sets via projections onto half-spaces

Journal of Approximation Theory
A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space

Journal of Approximation Theory
On the Mann-type iteration and the convex feasibility problem

Journal of Computational and Applied Mathematics
A new criterion for the inexact logarithmic-quadratic proximal method and its derived hybrid methods

Journal of Global Optimization
Convergence theorems for inertial KM-type algorithms

Journal of Computational and Applied Mathematics
A descent method for structured monotone variational inequalities

Optimization Methods & Software
Parallel algorithms for variational inequalities over the Cartesian product of the intersections of the fixed point sets of nonexpansive mappings

Journal of Approximation Theory
A Deep Monotone Approximation Operator Based on the Best Quadratic Lower Bound of Convex Functions

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
The viscosity approximation process for quasi-nonexpansive mappings in Hilbert spaces

Computers & Mathematics with Applications
Adaptive constrained learning in reproducing Kernel Hilbert spaces: the robust beamforming case

IEEE Transactions on Signal Processing
Proximal methods for a class of bilevel monotone equilibrium problems

Journal of Global Optimization
Some Goldstein's type methods for co-coercive variant variational inequalities

Applied Numerical Mathematics
Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces

Computers & Mathematics with Applications
A note on the regularized proximal point algorithm

Journal of Global Optimization
Convergence of Mann's type iteration method for generalized asymptotically nonexpansive mappings

Computers & Mathematics with Applications
Halpern-type iterations for strongly relatively nonexpansive mappings in Banach spaces

Computers & Mathematics with Applications
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations

SIAM Journal on Optimization
Algorithms for the Split Variational Inequality Problem

Numerical Algorithms
Viscosity approximations by the shrinking projection method in Hilbert spaces

Computers & Mathematics with Applications
On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints

Computational Optimization and Applications
Alternating Direction Method for Covariance Selection Models

Journal of Scientific Computing
Full length article: Attouch-Théra duality revisited: Paramonotonicity and operator splitting

Journal of Approximation Theory
Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective

SIAM Journal on Imaging Sciences
A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality

SIAM Journal on Optimization
Products of Finitely Many Resolvents of Maximal Monotone Mappings in Reflexive Banach Spaces

SIAM Journal on Optimization
On the contraction-proximal point algorithms with multi-parameters

Journal of Global Optimization
Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly. Exploiting an idea originally proposed by Haugazeau, we present a simple modification of these methods that makes them strongly convergent without additional assumptions. Several applications are discussed.