TY - JOUR
T1 - Alternating projection based prediction-correction methods for structured variational inequalities
AU - He, Bing Sheng
AU - Liao, Lizhi
AU - Qian, Mai Jian
N1 - Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.
PY - 2006/11
Y1 - 2006/11
N2 - 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.
AB - 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.
KW - Monotonicity
KW - Prediction-correction method
KW - Structured variational inequality
UR - http://www.global-sci.org/v1/jcm/volumes/v24n6/pdf/246-693.pdf?code=jOBTZztqO0DL5c%2ByZr3ypQ%3D%3D
UR - https://www.global-sci.org/intro/article_detail/jcm/8784.html
UR - http://www.scopus.com/inward/record.url?scp=33846143142&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:33846143142
SN - 0254-9409
VL - 24
SP - 693
EP - 710
JO - Journal of Computational Mathematics
JF - Journal of Computational Mathematics
IS - 6
ER -