Local convergence analysis of projection-type algorithms: unified approach

Authors:
N. H. Xiu;J. Z. Zhang
Affiliations:
Professor, Department of Applied Mathematics, Northern Jiaotong University, Beijing, PRC;Professor, Department of Mathematics, City University of Hong Kong, Hong Kong, PRC
Venue:
Journal of Optimization Theory and Applications
Year:
2002

Citing 28
Cited 4

Projected gradient methods for linearly constrained problems

Mathematical Programming: Series A and B
On the identification of active constraints

SIAM Journal on Numerical Analysis
Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications

Mathematical Programming: Series A and B
Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming

Mathematical Programming: Series A and B
Modification of the extra-gradient method for solving variational inequalities and certain optimization problems

USSR Computational Mathematics and Mathematical Physics
Applications of splitting algorithm to decomposition in convex programming and variational inequalities

SIAM Journal on Control and Optimization
Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems

Mathematical Programming: Series A and B
A globally convergent Newton method for solving strongly monotone variational inequalities

Mathematical Programming: Series A and B
A new method for a class of linear variational inequalities

Mathematical Programming: Series A and B
On linear convergence of iterative methods for the variational inequality problem

Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
Nondegenerate Solutions and Related Concepts in Affine Variational Inequalities

SIAM Journal on Control and Optimization
The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem

Mathematical Programming: Series A and B
Modified Projection-Type Methods for Monotone Variational Inequalities

SIAM Journal on Control and Optimization
A class of iterative methods for solving nonlinear projection equations

Journal of Optimization Theory and Applications
Family of projected descent methods for optimization problems with simple bounds

Journal of Optimization Theory and Applications
Proximal Minimization Methods with Generalized Bregman Functions

SIAM Journal on Control and Optimization
Nondegeneracy Concepts for Zeros of Piecewise Smooth Functions

Mathematics of Operations Research
Convergence Properties of Feasible Descent Methods for Solving Variational Inequalities in Banach Spaces

Computational Optimization and Applications
A New Projection Method for Variational Inequality Problems

SIAM Journal on Control and Optimization
A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings

SIAM Journal on Control and Optimization
Local convergence behavior of some projection-type methods for affine variational inequalities

Journal of Optimization Theory and Applications
Alternating Projection-Proximal Methods for Convex Programming and Variational Inequalities

SIAM Journal on Optimization
On the Accurate Identification of Active Constraints

SIAM Journal on Optimization
Weak Sharp Solutions of Variational Inequalities

SIAM Journal on Optimization
A Generalized Proximal Point Algorithm for the Variational Inequality Problem in a Hilbert Space

SIAM Journal on Optimization
An Active Set Newton Algorithm for Large-Scale Nonlinear Programs with Box Constraints

SIAM Journal on Optimization
Newton's Method for Large Bound-Constrained Optimization Problems

SIAM Journal on Optimization
Convergence Rates in Forward--Backward Splitting

SIAM Journal on Optimization

Some recent advances in projection-type methods for variational inequalities

Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Modified extragradient methods for solving variational inequalities

Computers & Mathematics with Applications
General approximation solvability of a system of strongly g-r-pseudomonotonic nonlinear variational inequalities and projection methods

Mathematical and Computer Modelling: An International Journal
Smoothing SQP algorithm for semismooth equations with box constraints

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we use a unified approach to analyze the local convergence behavior of a wide class of projection-type methods for solving variational inequality problems. Under certain conditions, it is shown that, in a finite number of iterations, either the sequence of iterates terminates at a solution of the concerned problem or all iterates enter and remain in the relative interior of the optimal face and, hence, the subproblem reduces to a simpler form.