Alternating projection based prediction-correction methods for structured variational inequalities

Bing Sheng He*, Lizhi LIAO, Mai Jian Qian

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

The monotone variational inequalities VI (Ω, F) have vast applications, including optimal controls and convex programming. In this paper we focus on the VI problems that have a particular splitting structure and in which the mapping F does not have an explicit form, therefore only its function values can be employed in the numerical methods for solving such problems. We study a set of numerical methods that are easily implement able. Each iteration of the proposed methods consists of two procedures. The first (prediction) procedure utilizes alternating projections to produce a predictor. The second (correction) procedure generates the new iterate via some minor computations. Convergence of the proposed methods is proved under mild conditions. Preliminary numerical experiments for some traffic equilibrium problems illustrate the effectiveness of the proposed methods.

Original languageEnglish
Pages (from-to)693-710
Number of pages18
JournalJournal of Computational Mathematics
Volume24
Issue number6
Publication statusPublished - Nov 2006

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Monotonicity
  • Prediction-correction method
  • Structured variational inequality

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