Mathematical Programming

, Volume 104, Issue 2, pp 749–760

A local minimax characterization for computing multiple nonsmooth saddle critical points

Article

DOI: 10.1007/s10107-005-0636-x

Cite this article as:
Yao, X. & Zhou, J. Math. Program. (2005) 104: 749. doi:10.1007/s10107-005-0636-x

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.

Keywords

Locally Lipschitz Continuous Functionals Nonsmooth Critical Points Minimax Characterization 

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege Station
  2. 2.Department of MathematicsUniversity of ConnecticutStorrsUSA
  3. 3.Department of MathematicsTexas A&M UniversityCollege StationUSA

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