ALTERNATING PROJECTION BASED PREDICTION-CORRECTION METHODS FOR STRUCTURED VARIATIONAL INEQUALITIES
ALTERNATING PROJECTION BASED PREDICTION-CORRECTION METHODS FOR STRUCTURED VARIATIONAL INEQUALITIES
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发表时间：
2006
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通讯作者：
B. He;L. Liao;M. Qian
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作者：
B. He;L. Liao;M. Qian
单调变分不等式VI（Ω， F）具有广泛的应用，包括最优控制和凸规划。本文主要研究具有特殊分裂结构的VI问题，其中映射F不具有显式形式，因此在求解这类问题的数值方法中只能采用其函数值。我们研究了一套易于实现的数值方法。所提方法的每次迭代由两个过程组成。第一个（预测）程序利用交替的预测来产生一个预测器。第二个（修正）过程通过一些小的计算生成新的迭代。在较温和的条件下证明了所提方法的收敛性。对一些交通平衡问题的初步数值实验表明了所提方法的有效性。数学学科分类：65K10、90C25、90C30。
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 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. Mathematics subject classification: 65K10, 90C25, 90C30.