Quadratic convergence analysis of a nonmonotone Levenberg–Marquardt type method for the weighted nonlinear complementarity problem

Jingyong Tang () and Jinchuan Zhou ()
Additional contact information
Jingyong Tang: Xinyang Normal University
Jinchuan Zhou: Shandong University of Technology

Computational Optimization and Applications, 2021, vol. 80, issue 1, No 8, 213-244

Abstract: Abstract In this paper we consider the weighted nonlinear complementarity problem (denoted by wNCP) which contains a wide class of optimization problems. We introduce a family of new weighted complementarity functions and show that it is continuously differentiable everywhere and has several favorable properties. Based on this function, we reformulate the wNCP as a smooth nonlinear equation and propose a nonmonotone Levenberg–Marquardt type method to solve it. We show that the proposed method is well-defined and it is globally convergent without any additional condition. Moreover, we prove that the whole iteration sequence converges to a solution of the wNCP locally superlinearly or quadratically under the nonsingularity condition. In addition, we establish the local quadratic convergence of the proposed method under the local error bound condition. Some numerical results are also reported.

Keywords: Weighted nonlinear complementarity problem; Levenberg–Marquardt method; Complementarity function; Local error bound; Quadratic convergence (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-021-00300-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:80:y:2021:i:1:d:10.1007_s10589-021-00300-8

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-021-00300-8

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().