Convergence of two-stage method with Bregman divergence for solving variational inequalities

DOI10.1007/s10559-019-00142-7zbMath1485.49018OpenAlexW2945578891MaRDI QIDQ2320219

Yanyan Li

Publication date: 22 August 2019

Published in: Cybernetics and Systems Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10559-019-00142-7

zbMATH Keywords

monotonicityconvergencevariational inequalityLipschitz conditiontwo-stage methodBregman divergencepseudo-monotonicity

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)

Related Items

Some Extragradient Methods for Solving Variational Inequalities Using Bregman Projection and Fixed Point Techniques in Reflexive Banach Spaces ⋮ A Novel Algorithm with Self-adaptive Technique for Solving Variational Inequalities in Banach Spaces ⋮ A Bregman subgradient extragradient method with self-adaptive technique for solving variational inequalities in reflexive Banach spaces ⋮ On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraints ⋮ Adaptive two-stage Bregman method for variational inequalities ⋮ Adaptive extraproximal algorithm for the equilibrium problem in Hadamard spaces ⋮ Bregman-Golden ratio algorithms for variational inequalities ⋮ Convergence of a two-stage proximal algorithm for the equilibrium problem in Hadamard spaces ⋮ An adaptive two-stage proximal algorithm for equilibrium problems in Hadamard spaces ⋮ Weak and strong convergence Bregman extragradient schemes for solving pseudo-monotone and non-Lipschitz variational inequalities ⋮ Bregman extragradient method with monotone rule of step adjustment ⋮ Bregman subgradient extragradient method with monotone self-adjustment stepsize for solving pseudo-monotone variational inequalities and fixed point problems ⋮ Convergence of the method of extrapolation from the past for variational inequalities in uniformly convex Banach spaces ⋮ Convergence of the operator extrapolation method for variational inequalities in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Low-cost modification of Korpelevich's methods for monotone equilibrium problems
• The subgradient extragradient method for solving variational inequalities in Hilbert space
• A version of the mirror descent method to solve variational inequalities
• Dual extrapolation and its applications to solving variational inequalities and related problems
• Convergence of the modified extragradient method for variational inequalities with non-Lipschitz operators
• Combined relaxation methods for variational inequalities
• Network economics: a variational inequality approach
• An extragradient algorithm for monotone variational inequalities
• Hybrid splitting methods for the system of operator inclusions with monotone operators
• Interior projection-like methods for monotone variational inequalities
• The Linearized Bregman Method via Split Feasibility Problems: Analysis and Generalizations
• A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming
• First-Order Methods in Optimization
• Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems
• The use of additional diminishing disturbances in Fejer models of iterative algorithms