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On finite convergence of proximal point algorithms for variational inequalities

Naihua Xiu, Jianzhong Zhang

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

Abstract

In this paper, we first characterize finite convergence of an arbitrary iterative algorithm for solving the variational inequality problem (VIP), where the finite convergence means that the algorithm can find an exact solution of the problem in a finite number of iterations. By using this result, we obtain that the well-known proximal point algorithm possesses finite convergence if the solution set of VIP is weakly sharp. As an extension, we show finite convergence of the inertial proximal method for solving the general variational inequality problem under the condition of weak g-sharpness. © 2005 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)148-158
JournalJournal of Mathematical Analysis and Applications
Volume312
Issue number1
DOIs
Publication statusPublished - 1 Dec 2005
Externally publishedYes

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 <a href="mailto:[email protected]">[email protected]</a>.

Funding

This research was partly supported by the CityU Strategic Research Grant (7001427), the National Natural Science Foundation of China (10271002, 70471002), and the Key Project of Chinese Ministry of Education (104048).

Research Keywords

  • Finite convergence
  • Inertial proximal method
  • Proximal point algorithm
  • Variational inequalities
  • Weak sharpness

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