Local convergence analysis of projection-type algorithms: Unified approach

N. H. Xiu; J. Z. Zhang

doi:10.1023/A:1019637315803

Local convergence analysis of projection-type algorithms: Unified approach

N. H. Xiu
, J. Z. Zhang

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

28 Citations (Scopus)

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.
© 2002 Plenum Publishing Corporation

Original language	English
Pages (from-to)	211-230
Journal	Journal of Optimization Theory and Applications
Volume	115
Issue number	1
DOIs	https://doi.org/10.1023/A:1019637315803
Publication status	Published - Oct 2002
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

This research was partly supported by the National Natural Science Foundation of China Grant 19971002 and by the City University of Hong Kong Strategic Research Grant 7001258.

Research Keywords

local convergence
projection methods
Variational inequalities

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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. {\textcopyright} 2002 Plenum Publishing Corporation",

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T2 - Unified approach

AU - Xiu, N. H.

AU - Zhang, J. Z.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2002/10

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N2 - 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. © 2002 Plenum Publishing Corporation

AB - 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. © 2002 Plenum Publishing Corporation

KW - local convergence

KW - projection methods

KW - Variational inequalities

UR - https://www.scopus.com/pages/publications/0036341174

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0036341174&origin=recordpage

U2 - 10.1023/A:1019637315803

DO - 10.1023/A:1019637315803

M3 - RGC 21 - Publication in refereed journal

SN - 0022-3239

VL - 115

SP - 211

EP - 230

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 1

ER -

Local convergence analysis of projection-type algorithms: Unified approach

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