Pang, Jong-Shi; Qi, Liqun Nonsmooth equations: Motivation and algorithms. (English) Zbl 0784.90082 SIAM J. Optim. 3, No. 3, 443-465 (1993). The paper is devoted to the generalization of Newton-type methods for solving nonsmooth equations. The authors give a generalization of the Dennis-Moré characterization of superlinearly converging quasi-Newton algorithms for semismooth mappings. They also establish the global convergence of a Gauss-Newton type algorithm for mappings satisfying some generalized regularity properties. Reviewer: J.F.Bonnans (Le Chesnay) Cited in 2 ReviewsCited in 164 Documents MSC: 90C30 Nonlinear programming 49J52 Nonsmooth analysis 26B10 Implicit function theorems, Jacobians, transformations with several variables 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 49J40 Variational inequalities Keywords:nonsmooth equations; superlinearly converging quasi-Newton algorithms; semismooth mappings; global convergence; Gauss-Newton type algorithm PDFBibTeX XMLCite \textit{J.-S. Pang} and \textit{L. Qi}, SIAM J. Optim. 3, No. 3, 443--465 (1993; Zbl 0784.90082) Full Text: DOI