摘要
变分不等式的三步松弛混合最速下降法(three-step RHSD method)在原条件和改进条件下均是强收敛的,并且在改进条件下的强收敛性证明更为简洁。本文通过对原条件和改进条件进行分析,得到了三步松弛混合最速下降法在改进条件下是本质上的混合最速下降。随后通过一系列的数值试验表明了三步松弛混合最速下降法在改进条件下比在原条件下更有效率。
Researchers have provided a three-step relaxed hybrid steepest-descent method(Three-step RHSD Method) for variational inequalities,and described the strong convergence of Three-step RHSD Method under some suitable conditions(Old Conditions).Subsequently,a simple proof of Three-step RHSD Method under some suitable modified conditions(Modified Conditions) was provided.In this paper,we show that the Three-step RHSD Method is substantially hybrid steepest-descent method under the Modified Conditions.Moreover,some practical numerical experiments and the results verify that the Three-step RHSD Method is more efficient under the Modified Conditions than under the Old Conditions.
出处
《科技通报》
北大核心
2013年第5期1-4,12,共5页
Bulletin of Science and Technology
基金
国家科技支撑项目(2011BAH24B06)
中国民航飞行学院科研基金(J2010-45)
国家自然科研基金联合基金项目(U1233105)
关键词
松弛混合最速下降法
变分不等式
强收敛
非扩张映射
relaxed hybxid steepest-descent method
variational inequality
strong convergence
non-expansive mapping
