Nonsmooth Equations: Motivation and Algorithms
- 1 August 1993
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 3 (3), 443-465
- https://doi.org/10.1137/0803021
Abstract
This paper reports on some recent developments in the area of solving of nonsmooth equations by generalized Newton methods. The emphasis is on three topics: motivation, characterization of superlinear convergence, and a new Gauss–Newton method for solving a certain class of nonsmooth equations. The characterization of superlinear convergence extends the classical result of Dennis and Moré for smooth equations and that of Ip and Kyparisis for B-differentiable equations. The Gauss–Newton method is different from that proposed recently by Han, Pang, and Rangaraj; it uses convex quadratic programs to generate descent directions for the least-squares merit function.Keywords
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