Improved convergence results for a modified Levenberg–Marquardt method for nonlinear equations and applications in MPCC. (3rd July 2016)

• Record Type: Journal Article
• Authors: Zhu, Xide; Lin, Gui-Hua
• Is Part Of: Optimization methods and software. Volume 31:Number 4(2016)
• Page Start: 791
• Page End: 804
• Publication Date: 2016-07-03
• Subjects: nonlinear equations -- Levenberg–Marquardt method -- MPCC -- C-/M-/S-stationarity -- superlinear convergence; 90C30 -- 90C33 -- 90C46; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2016.1171863
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we first consider a modified Levenberg–Marquardt method for solving nonlinear equations and show that the method converges superlinearly to a solution of the nonlinear equations under suitable conditions. Then, we reformulate the C-/M-/S-stationarity conditions of mathematical program with complementarity constraints as nonlinear equations so that we may employ the modified Levenberg–Marquardt method to solve these stationarity systems. Preliminary numerical experiments show that the new approach is promising.