Iterative methods for solving systems of variational inequalities in reflexive banach spaces

Gábor Kassay; Simeon Reich; Shoham Sabach

doi:10.1137/110820002

Iterative methods for solving systems of variational inequalities in reflexive banach spaces

Gábor Kassay, Simeon Reich, Shoham Sabach

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We prove strong convergence theorems for three iterative algorithms which approximate solutions to systems of variational inequalities for mappings of monotone type. All the theorems are set in reflexive Banach spaces and take into account possible computational errors.

Original language	English
Pages (from-to)	1319-1344
Number of pages	26
Journal	SIAM Journal on Optimization
Volume	21
Issue number	4
DOIs	https://doi.org/10.1137/110820002
State	Published - 2011

Keywords

Banach space
Bregman distance
Bregman firmly nonexpansive operator
Bregman inverse strongly monotone mapping
Bregman projection
Hemicontinuous mapping
Iterative algorithm
Legendre function
Monotone mapping
Pseudomonotone mapping
Totally convex function
Variational inequality

All Science Journal Classification (ASJC) codes

Software
Theoretical Computer Science

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10.1137/110820002

Cite this

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title = "Iterative methods for solving systems of variational inequalities in reflexive banach spaces",

abstract = "We prove strong convergence theorems for three iterative algorithms which approximate solutions to systems of variational inequalities for mappings of monotone type. All the theorems are set in reflexive Banach spaces and take into account possible computational errors.",

keywords = "Banach space, Bregman distance, Bregman firmly nonexpansive operator, Bregman inverse strongly monotone mapping, Bregman projection, Hemicontinuous mapping, Iterative algorithm, Legendre function, Monotone mapping, Pseudomonotone mapping, Totally convex function, Variational inequality",

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year = "2011",

doi = "10.1137/110820002",

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AU - Kassay, Gábor

AU - Reich, Simeon

AU - Sabach, Shoham

PY - 2011

Y1 - 2011

N2 - We prove strong convergence theorems for three iterative algorithms which approximate solutions to systems of variational inequalities for mappings of monotone type. All the theorems are set in reflexive Banach spaces and take into account possible computational errors.

AB - We prove strong convergence theorems for three iterative algorithms which approximate solutions to systems of variational inequalities for mappings of monotone type. All the theorems are set in reflexive Banach spaces and take into account possible computational errors.

KW - Banach space

KW - Bregman distance

KW - Bregman firmly nonexpansive operator

KW - Bregman inverse strongly monotone mapping

KW - Bregman projection

KW - Hemicontinuous mapping

KW - Iterative algorithm

KW - Legendre function

KW - Monotone mapping

KW - Pseudomonotone mapping

KW - Totally convex function

KW - Variational inequality

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U2 - 10.1137/110820002

DO - 10.1137/110820002

M3 - مقالة

SN - 1052-6234

VL - 21

SP - 1319

EP - 1344

JO - SIAM Journal on Optimization

JF - SIAM Journal on Optimization

IS - 4

ER -

Iterative methods for solving systems of variational inequalities in reflexive banach spaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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