Weakly sharp solutions and finite convergence of algorithms for a variational inequality problem

Yina Liu

doi:10.1080/02331934.2017.1397146

Weakly sharp solutions and finite convergence of algorithms for a variational inequality problem

Yina Liu^*

^*Corresponding author for this work

Department of Applied Mathematics

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

6 Citations (Scopus)

Abstract

The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using primal and dual gap functions, g and G, and also without considering gap functions, either. The subdifferential and locally Lipschitz properties of g + λG for λ > 0 are first studied since they are useful for discussing weakly sharp solutions of the variational inequality. A result of finite termination of a class of algorithms for solving the variational inequality problem is also studied.

Original language	English
Pages (from-to)	329-340
Number of pages	12
Journal	Optimization
Volume	67
Issue number	2
DOIs	https://doi.org/10.1080/02331934.2017.1397146
Publication status	Published - 1 Feb 2018

Keywords

Variational inequality
convergence of an algorithm
error bound
gap functions
gâteaux differentiable
locally Lipschitz property
weakly sharp solution

Access to Document

10.1080/02331934.2017.1397146

Cite this

Liu, Y. (2018). Weakly sharp solutions and finite convergence of algorithms for a variational inequality problem. Optimization, 67(2), 329-340. https://doi.org/10.1080/02331934.2017.1397146

@article{2960dc26d610446aab20945a9fb89ae1,

title = "Weakly sharp solutions and finite convergence of algorithms for a variational inequality problem",

abstract = "The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using primal and dual gap functions, g and G, and also without considering gap functions, either. The subdifferential and locally Lipschitz properties of g + λG for λ > 0 are first studied since they are useful for discussing weakly sharp solutions of the variational inequality. A result of finite termination of a class of algorithms for solving the variational inequality problem is also studied.",

keywords = "Variational inequality, convergence of an algorithm, error bound, gap functions, g{\^a}teaux differentiable, locally Lipschitz property, weakly sharp solution",

author = "Yina Liu",

note = "Publisher Copyright: {\textcopyright} 2017 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2018",

month = feb,

day = "1",

doi = "10.1080/02331934.2017.1397146",

language = "English",

volume = "67",

pages = "329--340",

journal = "Optimization",

issn = "0233-1934",

number = "2",

}

TY - JOUR

T1 - Weakly sharp solutions and finite convergence of algorithms for a variational inequality problem

AU - Liu, Yina

PY - 2018/2/1

Y1 - 2018/2/1

N2 - The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using primal and dual gap functions, g and G, and also without considering gap functions, either. The subdifferential and locally Lipschitz properties of g + λG for λ > 0 are first studied since they are useful for discussing weakly sharp solutions of the variational inequality. A result of finite termination of a class of algorithms for solving the variational inequality problem is also studied.

AB - The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using primal and dual gap functions, g and G, and also without considering gap functions, either. The subdifferential and locally Lipschitz properties of g + λG for λ > 0 are first studied since they are useful for discussing weakly sharp solutions of the variational inequality. A result of finite termination of a class of algorithms for solving the variational inequality problem is also studied.

KW - Variational inequality

KW - convergence of an algorithm

KW - error bound

KW - gap functions

KW - gâteaux differentiable

KW - locally Lipschitz property

KW - weakly sharp solution

UR - http://www.scopus.com/inward/record.url?scp=85032834894&partnerID=8YFLogxK

U2 - 10.1080/02331934.2017.1397146

DO - 10.1080/02331934.2017.1397146

M3 - Article

AN - SCOPUS:85032834894

SN - 0233-1934

VL - 67

SP - 329

EP - 340

JO - Optimization

JF - Optimization

IS - 2

ER -

Weakly sharp solutions and finite convergence of algorithms for a variational inequality problem

Abstract

Keywords

Access to Document

Other files and links

Cite this