A local minimax characterization for computing multiple nonsmooth saddle critical points Academic Article

abstract

• 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. Springer-Verlag 2005.

authors

• Zhou, Jianxin

published proceedings

• Mathematical Programming

author list (cited authors)

• Yao, X., & Zhou, J.

citation count

• 7

complete list of authors

• Yao, Xudong||Zhou, Jianxin

publication date

• November 2005

publisher

• Springer Nature  Publisher

published in

• Mathematical programming  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4903 Numerical And Computational Mathematics

Digital Object Identifier (DOI)

• 10.1007/s10107-005-0636-x

start page

• 749

end page

• 760

volume

• 104

issue

• 2-3

URL

• http://dx.doi.org/10.1007/s10107-005-0636-x