A local minimax characterization for computing multiple nonsmooth saddle critical points
成果类型：
Article
署名作者：
Yao, XD; Zhou, JX
署名单位：
Texas A&M University System; Texas A&M University College Station
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-005-0636-x
发表日期：
2005
页码：
749-760
关键词：
摘要：
This paper is concerned with characterizations of nonsmooth saddle critical points for numerical algorithm design. Most characterizations for nonsmooth saddle critical points in the literature focus on existence issue and are converted to solve global minimax problems. Thus they are not helpful for numerical algorithm design. Inspired by the results on computational theory and methods for finding multiple smooth saddle critical points in [14, 15, 19, 21, 23], a local minimax characterization for multiple nonsmooth saddle critical points in either a Hilbert space or a reflexive Banach space is established in this paper to provide a mathematical justification for numerical algorithm design. A local minimax algorithm for computing multiple nonsmooth saddle critical points is presented by its flow chart.