Bounded perturbation resilience of extragradient-type methods and their applications

DOI10.1186/s13660-017-1555-0zbMath1378.49026arXiv1711.01937OpenAlexW2963022965WikidataQ47158993 ScholiaQ47158993MaRDI QIDQ1677995

Peng Zhang

Publication date: 14 November 2017

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.01937

zbMATH Keywords

variational inequalityextragradient methodbounded perturbation resiliencesubgradient extragradient methodinertial-type method

Mathematics Subject Classification ID

Minimax problems in mathematical programming (90C47) Variational inequalities (49J40) Newton-type methods (49M15) Existence of solutions for minimax problems (49J35) Variational inequalities (global problems) in infinite-dimensional spaces (58E35) Numerical methods for variational inequalities and related problems (65K15)

Related Items (8)

A new efficient algorithm for finding common fixed points of multivalued demicontractive mappings and solutions of split generalized equilibrium problems in Hilbert spaces ⋮ Outer perturbations of a projection method and two approximation methods for the split equality problem ⋮ Convergence of a subgradient extragradient algorithm for solving monotone variational inequalities ⋮ Bounded perturbation resilience and superiorization techniques for a modified proximal gradient method ⋮ Total variation superiorized conjugate gradient method for image reconstruction ⋮ Accelerating two projection methods via perturbations with application to intensity-modulated radiation therapy ⋮ A new inertial double-projection method for solving variational inequalities ⋮ Self adaptive inertial subgradient extragradient algorithms for solving pseudomonotone variational inequality problems

Uses Software

• iPiasco

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Construction algorithms for a class of monotone variational inequalities
• The subgradient extragradient method for solving variational inequalities in Hilbert space
• Iterative algorithms for general multivalued variational inequalities
• iPiasco: inertial proximal algorithm for strongly convex optimization
• Strict Fejér monotonicity by superiorization of feasibility-seeking projection methods
• The extragradient algorithm with inertial effects for solving the variational inequality
• Self-adaptive projection methods for the multiple-sets split feasibility problem
• Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space
• Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space
• A Hybrid Proximal-Extragradient Algorithm with Inertial Effects
• Stable Convergence Theorems for Infinite Products and Powers of Nonexpansive Mappings
• Image reconstruction from a small number of projections
• Perturbation resilience and superiorization of iterative algorithms
• Modification of the extra-gradient method for solving variational inequalities and certain optimization problems
• Monotone Operators and the Proximal Point Algorithm
• Iterative algorithms for the split variational inequality and fixed point problems under nonlinear transformations
• Well-posedness for systems of time-dependent hemivariational inequalities in Banach spaces
• Weak Convergence of a Relaxed and Inertial Hybrid Projection-Proximal Point Algorithm for Maximal Monotone Operators in Hilbert Space
• Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems
• On Projection Algorithms for Solving Convex Feasibility Problems
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• A Dynamical Approach to an Inertial Forward-Backward Algorithm for Convex Minimization
• Minimum-norm solution of variational inequality and fixed point problem in banach spaces
• Asymptotic Behavior of Inexact Orbits for a Class of Operators in Complete Metric Spaces
• Some methods of speeding up the convergence of iteration methods
• Convex analysis and monotone operator theory in Hilbert spaces

This page was built for publication: Bounded perturbation resilience of extragradient-type methods and their applications