Projection methods with alternating inertial steps for variational inequalities: weak and linear convergence

DOI10.1016/j.apnum.2020.06.009zbMath1445.49004OpenAlexW3038106246MaRDI QIDQ2192627

Yekini Shehu, Olaniyi Samuel Iyiola

Publication date: 17 August 2020

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2020.06.009

zbMATH Keywords

variational inequalityprojection methodspseudo-monotone operatoralternated inertial

Mathematics Subject Classification ID

Variational inequalities (49J40) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items

Convergence analysis and applications of the inertial algorithm solving inclusion problems, Self-adaptive inertial single projection methods for variational inequalities involving non-Lipschitz and Lipschitz operators with their applications to optimal control problems, Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications, Regularization proximal method for monotone variational inclusions, Convergence analysis of new inertial method for the split common null point problem, An alternated inertial method for pseudomonotone variational inequalities in Hilbert spaces, Self-adaptive subgradient extragradient-type methods for solving variational inequalities, Revisiting the extragradient method for finding the minimum-norm solution of non-Lipschitzian pseudo-monotone variational inequalities, Revisiting subgradient extragradient methods for solving variational inequalities, Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems, Weak and linear convergence of a generalized proximal point algorithm with alternating inertial steps for a monotone inclusion problem, Inertial extragradient type method for mixed variational inequalities without monotonicity, Accelerated non-monotonic explicit proximal-type method for solving equilibrium programming with convex constraints and its applications, Inertial version of generalized projected reflected gradient method, Inertial relaxed CQ algorithm for split feasibility problems with non-Lipschitz gradient operators, An alternated inertial general splitting method with linearization for the split feasibility problem, An accelerated subgradient extragradient algorithm for solving bilevel variational inequality problems involving non-Lipschitz operator, Linearized Douglas-Rachford method for variational inequalities with Lipschitz mappings, Alternated and multi-step inertial approximation methods for solving convex bilevel optimization problems, Modified inertial extragradient methods for finding minimum-norm solution of the variational inequality problem with applications to optimal control problem, Modified inertial subgradient extragradient method for equilibrium problems, Alternated inertial algorithms for split feasibility problems, A modified generalized version of projected reflected gradient method in Hilbert spaces, A relaxed forward-backward-forward algorithm with alternated inertial step: weak and linear convergence, Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications, Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications, A simple projection method for solving quasimonotone variational inequality problems, Modified subgradient extragradient algorithms with a new line-search rule for variational inequalities, Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities, Inertial‐like Bregman projection method for solving systems of variational inequalities, Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems, Relaxed single projection methods for solving bilevel variational inequality problems in Hilbert spaces, Double inertial forward-backward-forward method with adaptive step-size for variational inequalities with quasi-monotonicity, Unnamed Item, Global and linear convergence of alternated inertial methods for split feasibility problems, Unnamed Item, An accelerated extragradient algorithm for bilevel pseudomonotone variational inequality problems with application to optimal control problems, A general inertial projected gradient method for variational inequality problems, An algorithm for approximating solutions of variational inequality and split fixed point problems with applications, Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems, Explicit extragradient-like method with adaptive stepsizes for pseudomonotone variational inequalities, Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators, Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators, Two adaptive modified subgradient extragradient methods for bilevel pseudomonotone variational inequalities with applications, New inertial forward-backward type for variational inequalities with quasi-monotonicity, A relaxed inertial factor of the modified subgradient extragradient method for solving pseudo monotone variational inequalities in Hilbert spaces, Inertial projection and contraction algorithms with larger step sizes for solving quasimonotone variational inequalities, Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems, Viscosity \(S\)-iteration method with inertial technique and self-adaptive step size for split variational inclusion, equilibrium and fixed point problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the \(O(1/t)\) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators
• Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces
• The subgradient extragradient method for solving variational inequalities in Hilbert space
• An approximate proximal-extragradient type method for monotone variational inequalities
• Weak convergence of an iterative method for pseudomonotone variational inequalities and fixed-point problems
• Convergence of one-step projected gradient methods for variational inequalities
• Modified projection method for strongly pseudomonotone variational inequalities
• Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems
• Combined relaxation method for generalized variational inequalities
• Inertial projection and contraction algorithms for variational inequalities
• On the weak convergence of the extragradient method for solving pseudo-monotone variational inequalities
• On the proximal gradient algorithm with alternated inertia
• Iterative methods for pseudomonotone variational inequalities and fixed-point problems
• The forward-backward-forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces
• A class of projection and contraction methods for monotone variational inequalities
• An extragradient-like approximation method for variational inequality problems and fixed point problems
• Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings
• Forcing strong convergence of Korpelevich's method in Banach spaces with its applications in game theory
• Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space
• Application Of Khobotov’s Algorithm To Variational Inequalities And Network Equilibrium Problems
• Modification of the extra-gradient method for solving variational inequalities and certain optimization problems
• A New Projection Method for Variational Inequality Problems
• A variant of korpelevich’s method for variational inequalities with a new search strategy
• Single projection method for pseudo-monotone variational inequality in Hilbert spaces
• Two simple relaxed perturbed extragradient methods for solving variational inequalities in Euclidean spaces
• A generic online acceleration scheme for optimization algorithms via relaxation and inertia
• An Introduction to Numerical Analysis
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
• A modified Korpelevich's method convergent to the minimum-norm solution of a variational inequality
• Optimal Convergence Rates for Nesterov Acceleration
• Projected Reflected Gradient Methods for Monotone Variational Inequalities
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Convex analysis and monotone operator theory in Hilbert spaces