A projected subgradient algorithm for bilevel equilibrium problems and applications
type: Item
instance of: scholarly article
title: A projected subgradient algorithm for bilevel equilibrium problems and applications
zbMATH Open document ID: 1382.65182
author: Le Quang Thuy
author: Trinh Ngoc Hai
published in: Journal of Optimization Theory and Applications
publication date: 2017-12-15T00:00:00Z
review text: A new computational method is proposed to solve bilevel equilibrium problems in a real Hilbert space. The algorithm is designed such that subgradients of two convex functions and one projection onto a convex set are computed at each iteration. As consequence, the procedure provided by the authors has a low computational cost. Some numerical experiments illustrate the convergence of the algorithm. The procedure is particularized on the equilibrium problem over a fixed point set.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 6819191
zbMATH Keywords: bilevel equilibrium problems
zbMATH Keywords: subgradient method
zbMATH Keywords: projection method
zbMATH Keywords: strong monotonicity
zbMATH Keywords: pseudoparamonotonicity
zbMATH Keywords: algorithm
zbMATH Keywords: numerical experiments
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: s10957-017-1176-2
OpenAlex ID: W2764267352
cites work: Q4057217
cites work: Q4236159
cites work: An inexact subgradient algorithm for equilibrium problems
cites work: Q4366516
cites work: Convergence of an adaptive penalty scheme for finding constrained equilibria
cites work: Q4110807
cites work: Extragradient algorithms extended to equilibrium problems¶
cites work: Modified Projection-Type Methods for Monotone Variational Inequalities
cites work: Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces
cites work: Parallel hybrid iterative methods for variational inequalities, equilibrium problems, and common fixed point problems
cites work: On ergodic algorithms for equilibrium problems
cites work: Two new splitting algorithms for equilibrium problems
cites work: Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings
cites work: A subgradient-type method for the equilibrium problem over the fixed point set and its applications
cites work: An iterative method for finding common solutions of equilibrium and fixed point problems
cites work: Modified hybrid projection methods for finding common solutions to variational inequality problems
cites work: Iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings
cites work: A hybrid subgradient algorithm for nonexpansive mappings and equilibrium problems
cites work: Fixed point optimization algorithm and its application to power control in CDMA data networks
cites work: Methods for Variational Inequality Problem Over the Intersection of Fixed Point Sets of Quasi-Nonexpansive Operators
cites work: Foundations of bilevel programming
cites work: Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints
cites work: Optimality conditions for bilevel programming problems
cites work: Bilevel Optimization as a Regularization Approach to Pseudomonotone Equilibrium Problems
cites work: A new iterative algorithm for the variational inequality problem over the fixed point set of a firmly nonexpansive mapping
cites work: A Use of Conjugate Gradient Direction for the Convex Optimization Problem over the Fixed Point Set of a Nonexpansive Mapping
cites work: Optimization over equilibrium sets∗
cites work: Parallel algorithms for variational inequalities over the Cartesian product of the intersections of the fixed point sets of nonexpansive mappings
cites work: The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings
cites work: A splitting algorithm for a class of bilevel equilibrium problems involving nonexpansive mappings
cites work: Projected subgradient techniques and viscosity methods for optimization with variational inequality constraints
cites work: An algorithm for a class of split feasibility problems: application to a model in electricity production
cites work: Q2997134
cites work: Application of the proximal point method to nonmonotone equilibrium problems
cites work: Regularization algorithms for solving monotone Ky Fan inequalities with application to a Nash-Cournot equilibrium model
cites work: The interior proximal extragradient method for solving equilibrium problems
cites work: Quasi-Fejérian analysis of some optimization algorithms
cites work: Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
cites work: Q4340161
cites work: Dual extragradient algorithms extended to equilibrium problems
DOI: 10.1007/S10957-017-1176-2
description: scientific article; zbMATH DE number 6819191