基于 PPA 的求解逆变分不等式方法
首发时间:2006-06-12
摘要:本文考虑一类逆变分不等式问题: 与普通的变分不等式不同的是, 其中的映射F(u),代替了原来的变量u, 被限制在一个闭凸集合内。 逆变分不等式来源于大量的系统控制问题,其中u是控制变量,而F(u)则是相应的系统状态。一般说来,在实际应用中,F(u)是单调的。为解决这类单调逆变分不等式问题, 本文提出一类临近点算法 (PPA) 及其不精确形式, 并在此基础上,提供了一种只需要知道函数值F(u)的自适应求解方法。
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PPA-based methods for monotone inverse variational inequalities
Abstract:We consider a class of inverse variational inequalities: unlike the regular variational inequalities, the mapping F(u), instead of the variable u, is restricted in a closed convex set. Inverse variational inequalities arise from various system control problems, where u is a control variable and F(u) is the relevant system status. In some applications, the mapping F(u) is monotone. For solving monotone inverse variational inequalities, this paper presents the proximal point algorithm (PPA) and its inexact versions. Finally, we present a PPA-based self-adaptive method that only needs the function value F(u) for given variables.
Keywords: Inverse variational inequality, monotone mapping, proximal point algorithm
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No.7096930661150109****
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