An Outer Approximation Method for the Variational Inequality Problem
From MaRDI portal
Publication:5317109
DOI10.1137/S0363012902415487zbMath1076.49003WikidataQ58048581 ScholiaQ58048581MaRDI QIDQ5317109
Regina Sandra Burachik, Jurandir O. Lopes, Benar Fux Svaiter
Publication date: 15 September 2005
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Banach spacesmaximal monotone operatorsvariational inequalitiesouter approximation algorithmsemi-infinite programs
Numerical mathematical programming methods (65K05) Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Monotone operators and generalizations (47H05) Numerical methods based on nonlinear programming (49M37) Semi-infinite programming (90C34) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)
Related Items
Some new extragradient-like methods for generalized equilibrium problems, fixed point problems and variational inequality problems ⋮ A relaxed-projection splitting algorithm for variational inequalities in Hilbert spaces ⋮ An inertial subgradient extragradient algorithm with adaptive stepsizes for variational inequality problems ⋮ Implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and Lipschitz-continuous monotone mappings ⋮ Hybrid approximate proximal method with auxiliary variational inequality for vector optimization ⋮ Strong convergence theorems for solving generalized mixed equilibrium problems and general system of variational inequalities by the hybrid method ⋮ A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces ⋮ New outer proximal methods for solving variational inequality problems ⋮ Self-adaptive gradient projection algorithms for variational inequalities involving non-Lipschitz continuous operators ⋮ Strong convergence theorems for variational inequalities and fixed point problems of asymptotically strict pseudocontractive mappings in the intermediate sense ⋮ Outer approximation algorithms for pseudomonotone equilibrium problems ⋮ Hybrid extragradient iterative algorithms for variational inequalities, variational inclusions, and fixed-point problems ⋮ Strong convergence theorems of the \(C Q\) algorithm for \(H\)-monotone operators in Hilbert spaces ⋮ Approximate proximal algorithms for generalized variational inequalities with paramonotonicity and pseudomonotonicity ⋮ A new hybrid projection algorithm for solving the split generalized equilibrium problems and the system of variational inequality problems ⋮ Iterative approximation of countable family of relatively nonexpansive mappings and system of equilibrium problems in Banach spaces ⋮ Iterative algorithm by using the hybrid method in mathematical programming for solving variational inequality problems and equilibrium problems ⋮ An implicit iterative scheme for monotone variational inequalities and fixed point problems ⋮ An inexact proximal-type method for the generalized variational inequality in Banach spaces ⋮ Numerical approach to monotone variational inequalities by a one-step projected reflected gradient method with line-search procedure ⋮ Approximate proximal algorithms for generalized variational inequalities with pseudomonotone multifunctions ⋮ Outer approximation schemes for generalized semi-infinite variational inequality problems ⋮ Convergence analysis of a hybrid Mann iterative scheme with perturbed mapping for variational inequalities and fixed point problems ⋮ Convergence of one-step projected gradient methods for variational inequalities ⋮ A projected extrapolated gradient method with larger step size for monotone variational inequalities ⋮ Explicit extragradient-like method with adaptive stepsizes for pseudomonotone variational inequalities ⋮ Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space ⋮ A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping ⋮ An Algorithm Using Trust Region Strategy for Minimization of a Nondifferentiable Function
