A new low-cost double projection method for solving variational inequalities

DOI10.1007/s11081-020-09490-2zbMath1456.65190OpenAlexW3006370257MaRDI QIDQ2218909

Aviv Gibali, Duong Viet Thong

Publication date: 18 January 2021

Published in: Optimization and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11081-020-09490-2

zbMATH Keywords

variational inequality problemPopov's methodpseudo-monotone mappingstrongly pseudo-monotone mapping

Mathematics Subject Classification ID

Variational inequalities (49J40) Iterative procedures involving nonlinear operators (47J25) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical methods for variational inequalities and related problems (65K15)

Related Items

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 ⋮ An inertial Popov's method for solving pseudomonotone variational inequalities ⋮ A Novel Algorithm with Self-adaptive Technique for Solving Variational Inequalities in Banach Spaces ⋮ A new Bregman projection method with a self-adaptive process for solving variational inequality problem in reflexive Banach spaces ⋮ A new low-cost feasible projection algorithm for pseudomonotone variational inequalities ⋮ A fully adaptive method for variational inequalities with quasi-monotonicity ⋮ Convergence analysis of a new Bregman extragradient method for solving fixed point problems and variational inequality problems in reflexive Banach spaces ⋮ Strong convergence theorem for a new Bregman extragradient method with a different line-search process for solving variational inequality problems in reflexive Banach spaces ⋮ A new Halpern-type Bregman projection method for solving variational inequality problems in reflexive Banach space ⋮ A new modified extragradient method with line-search process for solving pseudomonotone variational inequality in Hilbert spaces ⋮ Novel projection methods for solving variational inequality problems and 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 ⋮ Double inertial projection method for variational inequalities with quasi-monotonicity ⋮ Double inertial forward-backward-forward method with adaptive step-size for variational inequalities with quasi-monotonicity ⋮ Unnamed Item ⋮ Unnamed Item ⋮ New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings ⋮ Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems ⋮ 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 ⋮ New inertial forward-backward type for variational inequalities with quasi-monotonicity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Parallel hybrid iterative methods for variational inequalities, equilibrium problems, and common fixed point problems
• Special issue on applications of variational inequality problems
• Iterative methods for fixed point problems in Hilbert spaces
• On the \(O(1/t)\) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators
• Low-cost modification of Korpelevich's methods for monotone equilibrium problems
• Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces
• A hybrid method without extrapolation step for solving variational inequality problems
• The subgradient extragradient method for solving variational inequalities in Hilbert space
• Korpelevich's method for variational inequality problems in Banach spaces
• Modified projection method for strongly pseudomonotone variational inequalities
• Convergence of the modified extragradient method for variational inequalities with non-Lipschitz operators
• Pseudo-monotone complementarity problems in Hilbert space
• Combined relaxation methods for variational inequalities
• New extragradient-like algorithms for strongly pseudomonotone variational inequalities
• A modified projected gradient method for monotone variational inequalities
• Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery
• Strong convergence of a double projection-type method for monotone variational inequalities in Hilbert spaces
• On the weak convergence of the extragradient method for solving pseudo-monotone variational inequalities
• An extragradient algorithm for monotone variational inequalities
• Convergence of an extragradient-type method for variational inequality with applications to optimal control problems
• Modified extragradient-like algorithms with new stepsizes for variational inequalities
• A New Extragradient Method for Strongly Pseudomonotone Variational Inequalities
• 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 Extragradient-Viscosity Method for Monotone Operators and Fixed Point Problems
• A New Projection Method for Variational Inequality Problems
• A variant of korpelevich’s method for variational inequalities with a new search strategy
• Modified subgradient extragradient algorithms for solving monotone variational inequalities
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• Quasi-Variational Inequalities in Banach Spaces: Theory and Augmented Lagrangian Methods
• 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