Weak convergence of explicit extragradient algorithms for solving equilibrium problems

DOI10.1186/s13660-019-2233-1zbMath1499.49048OpenAlexW2988348752WikidataQ126863778 ScholiaQ126863778MaRDI QIDQ2068068

Habib ur Rehman, Pasakorn Yordsorn, Yeol Je Cho, Poom Kumam

Publication date: 19 January 2022

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

Full work available at URL: https://doi.org/10.1186/s13660-019-2233-1

zbMATH Keywords

equilibrium problemextragradient methodLipschitz-type conditionsNash-Cournot equilibrium model of electricity markets

Mathematics Subject Classification ID

Convex programming (90C25) Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

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Cites Work

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• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions
• An interior proximal cutting hyperplane method for equilibrium problems
• The subgradient extragradient method for solving variational inequalities in Hilbert space
• Convergence of hybrid steepest-descent methods for variational inequalities
• Outer approximation algorithms for pseudomonotone equilibrium problems
• Dual extragradient algorithms extended to equilibrium problems
• Auxiliary problem principle and decomposition of optimization problems
• Equilibrium models and variational inequalities.
• On ergodic algorithms for equilibrium problems
• Auxiliary problem principle extended to variational inequalities
• A modification of the Arrow-Hurwicz method for search of saddle points
• Equilibrium programming using proximal-like algorithms
• Combined relaxation method for generalized variational inequalities
• An inertial-like proximal algorithm for equilibrium problems
• New inertial algorithm for a class of equilibrium problems
• Weak and strong convergence of an inertial proximal method for solving Ky Fan minimax inequalities
• The new extragradient method extended to equilibrium problems
• A class of projection and contraction methods for monotone variational inequalities
• Halpern subgradient extragradient method extended to equilibrium problems
• Modified basic projection methods for a class of equilibrium problems
• Explicit iterative algorithms for solving equilibrium problems
• An Armijo-type method for pseudomonotone equilibrium problems and its applications
• Generalized monotone bifunctions and equilibrium problems
• The extragradient algorithm with inertial effects for solving the variational inequality
• A PROXIMAL POINT-TYPE ALGORITHM FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS
• The Bruck's ergodic iteration method for the Ky Fan inequality over the fixed point set
• Convergence of New Inertial Proximal Methods for DC Programming
• Projection methods for variational inequalities with application to the traffic assignment problem
• Convergence of an adaptive penalty scheme for finding constrained equilibria
• Monotone Operators and the Proximal Point Algorithm
• Single projection method for pseudo-monotone variational inequality in Hilbert spaces
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
• The subgradient extragradient method extended to equilibrium problems
• PARALLEL EXTRAGRADIENT-PROXIMAL METHODS FOR SPLIT EQUILIBRIUM PROBLEMS
• Extragradient algorithms extended to equilibrium problems¶
• Some methods of speeding up the convergence of iteration methods
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Convex analysis and monotone operator theory in Hilbert spaces
• An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping