A quasi-Newton modified LP-Newton method. (4th May 2019)

• Record Type: Journal Article
• Authors: Martínez, María de los Ángeles; Fernández, Damián
• Is Part Of: Optimization methods and software. Volume 34:Number 3(2019)
• Page Start: 634
• Page End: 649
• Publication Date: 2019-05-04
• Subjects: constrained nonlinear system of equations -- nonisolated solutions -- quasi-Newton method -- local convergence; 90C30 -- 65K05; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2017.1384955
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : We consider a method to solve constrained system of nonlinear equations based on a modification of the Linear-Programming-Newton method and replacing the first-order information with a quasi-Newton secant update, providing a computationally simple method. The proposed strategy combines good properties of two methods: the least change secant update for unconstrained system of nonlinear equations with isolated solutions and the Linear-Programming-Newton for constrained nonlinear system of equations with possible nonisolated solutions. We analyse the local convergence of the proposed method under a standard error bound condition proving its linear convergence for nonisolated solutions. Numerical experiments were done in order to show the claimed convergence rate.