摘要
对于广义Brouwer不动点问题的无界情形,研究者们主要针对凸集进行了一些研究,非凸集合还很少涉及。本文针对一类非凸集合,利用不动点问题的自映射以及新引入的二次连续可微映射构造了一组无界性条件,使得连续化方法能够求解无界非凸集合上的广义Brouwer不动点问题,并取得了该方法的全局收敛性结果,从而导致了可数值实现的全局收敛性算法。本文的研究结果在较大程度上推广了已有的研究结果,使得连续化方法能够处理更大一类不动点问题。
For the general Brouwer fixed point problems, the researchers mainly carry out a series of re- search work on nonconvex sets and get a lot of significant research results. For the unbounded cases, their research mainly involve convex sets and seldom nonconvex sets. In this paper, we used the self-mapping and the newly introduce twice continuously differentiable mapping to construct a set of unboundedness conditions and hence made the continuation method solve the general Brouwer fixed point problems on un- bounded nonconvex sets. Under suitable conditions, we got the global convergence results of the continu- ation method, which could lead to an implementable globally convergent algorithm. Our results improve the previous results greatly, so we make the continuation method to solve a broader class of fixed point problems.
出处
《中国海洋大学学报（自然科学版）》
CAS
CSCD
北大核心
2012年第11期123-126,共4页
Periodical of Ocean University of China
基金
中国海洋大学青年教师专项基金项目(201113008)
河南省基础与前沿技术研究项目(122300410261)资助
关键词
连续化方法
全局收敛性算法
不动点问题
continuation method
globally convergent algorithm
fixed point problems
