Finite convergence analysis and weak sharp solutions for variational inequalities

Suliman Al-Homidan; Qamrul Hasan Ansari; Luong Van Nguyen

doi:10.1007/s11590-016-1076-7

Finite convergence analysis and weak sharp solutions for variational inequalities

Suliman Al-Homidan
, Qamrul Hasan Ansari^*
, Luong Van Nguyen

^*Corresponding author for this work

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

19 Scopus citations

Abstract

In this paper, we study the weak sharpness of the solution set of variational inequality problem (in short, VIP) and the finite convergence property of the sequence generated by some algorithm for finding the solutions of VIP. In particular, we give some characterizations of weak sharpness of the solution set of VIP without considering the primal or dual gap function. We establish an abstract result on the finite convergence property for a sequence generated by some iterative methods. We then apply such abstract result to discuss the finite termination property of the sequence generated by proximal point method, exact proximal point method and gradient projection method. We also give an estimate on the number of iterates by which the sequence converges to a solution of the VIP.

Original language	English
Pages (from-to)	1647-1662
Number of pages	16
Journal	Optimization Letters
Volume	11
Issue number	8
DOIs	https://doi.org/10.1007/s11590-016-1076-7
State	Published - 1 Dec 2017

Bibliographical note

Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

Keywords

Exact proximal point method
Finite convergence analysis
Gap functions
Gradient projection method
Variational inequalities
Weak sharp solutions

ASJC Scopus subject areas

Control and Optimization

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10.1007/s11590-016-1076-7

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title = "Finite convergence analysis and weak sharp solutions for variational inequalities",

abstract = "In this paper, we study the weak sharpness of the solution set of variational inequality problem (in short, VIP) and the finite convergence property of the sequence generated by some algorithm for finding the solutions of VIP. In particular, we give some characterizations of weak sharpness of the solution set of VIP without considering the primal or dual gap function. We establish an abstract result on the finite convergence property for a sequence generated by some iterative methods. We then apply such abstract result to discuss the finite termination property of the sequence generated by proximal point method, exact proximal point method and gradient projection method. We also give an estimate on the number of iterates by which the sequence converges to a solution of the VIP.",

keywords = "Exact proximal point method, Finite convergence analysis, Gap functions, Gradient projection method, Variational inequalities, Weak sharp solutions",

author = "Suliman Al-Homidan and Ansari, \{Qamrul Hasan\} and \{Van Nguyen\}, Luong",

note = "Publisher Copyright: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",

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doi = "10.1007/s11590-016-1076-7",

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TY - JOUR

T1 - Finite convergence analysis and weak sharp solutions for variational inequalities

AU - Al-Homidan, Suliman

AU - Ansari, Qamrul Hasan

AU - Van Nguyen, Luong

PY - 2017/12/1

Y1 - 2017/12/1

N2 - In this paper, we study the weak sharpness of the solution set of variational inequality problem (in short, VIP) and the finite convergence property of the sequence generated by some algorithm for finding the solutions of VIP. In particular, we give some characterizations of weak sharpness of the solution set of VIP without considering the primal or dual gap function. We establish an abstract result on the finite convergence property for a sequence generated by some iterative methods. We then apply such abstract result to discuss the finite termination property of the sequence generated by proximal point method, exact proximal point method and gradient projection method. We also give an estimate on the number of iterates by which the sequence converges to a solution of the VIP.

AB - In this paper, we study the weak sharpness of the solution set of variational inequality problem (in short, VIP) and the finite convergence property of the sequence generated by some algorithm for finding the solutions of VIP. In particular, we give some characterizations of weak sharpness of the solution set of VIP without considering the primal or dual gap function. We establish an abstract result on the finite convergence property for a sequence generated by some iterative methods. We then apply such abstract result to discuss the finite termination property of the sequence generated by proximal point method, exact proximal point method and gradient projection method. We also give an estimate on the number of iterates by which the sequence converges to a solution of the VIP.

KW - Exact proximal point method

KW - Finite convergence analysis

KW - Gap functions

KW - Gradient projection method

KW - Variational inequalities

KW - Weak sharp solutions

UR - https://www.scopus.com/pages/publications/84984813567

U2 - 10.1007/s11590-016-1076-7

DO - 10.1007/s11590-016-1076-7

M3 - Article

AN - SCOPUS:84984813567

SN - 1862-4472

VL - 11

SP - 1647

EP - 1662

JO - Optimization Letters

JF - Optimization Letters

IS - 8

ER -

Finite convergence analysis and weak sharp solutions for variational inequalities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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