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Volume 24, Issue 6
Alternating Projection Based Prediction-Correction Methods for Structured Variational Inequalities

Bing-sheng He, Li-zhi Liao & Mai-jian Qian

J. Comp. Math., 24 (2006), pp. 693-710.

Published online: 2006-12

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  • Abstract

The monotone variational inequalities VI$(\Omega,F)$ 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 implementable. 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.

  • Keywords

Structured variational inequality, Monotonicity, Prediction-correction method.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JCM-24-693, author = {Bing-sheng He, Li-zhi Liao and Mai-jian Qian}, title = {Alternating Projection Based Prediction-Correction Methods for Structured Variational Inequalities}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {6}, pages = {693--710}, abstract = {

The monotone variational inequalities VI$(\Omega,F)$ 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 implementable. 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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8784.html} }
TY - JOUR T1 - Alternating Projection Based Prediction-Correction Methods for Structured Variational Inequalities AU - Bing-sheng He, Li-zhi Liao & Mai-jian Qian JO - Journal of Computational Mathematics VL - 6 SP - 693 EP - 710 PY - 2006 DA - 2006/12 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8784.html KW - Structured variational inequality, Monotonicity, Prediction-correction method. AB -

The monotone variational inequalities VI$(\Omega,F)$ 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 implementable. 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.

Bing-sheng He, Li-zhi Liao and Mai-jian Qian. (2006). Alternating Projection Based Prediction-Correction Methods for Structured Variational Inequalities. Journal of Computational Mathematics. 24 (6). 693-710. doi:
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