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Approximate norm descent methods for constrained nonlinear systems

Benedetta Morini (benedetta.morini***at***unifi.it)
Margherita Porcelli (margherita.porcelli***at***unifi.it)
Philippe L. Toint (philippe.toint***at***unamur.be)

Abstract: We address the solution of convex-constrained nonlinear systems of equations where the Jacobian matrix is unavailable or its computation/storage is burdensome. In order to efficiently solve such problems, we propose a new class of algorithms which are ``derivative-free'' both in the computation of the search direction and in the selection of the steplength. Search directions comprise the residuals and Quasi-Newton directions while the steplength is determined by using a new linesearch strategy based on a nonmonotone approximate norm descent property of the merit function. We provide a theoretical analysis of the proposed algorithm and we discuss several conditions ensuring convergence to a solution of the constrained nonlinear system. Finally, we illustrate its numerical behaviour also in comparison with existing approaches.

Keywords: nonlinear systems of equations, convex constraints, numerical algorithms, convergence theory

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Category 2: Nonlinear Optimization (Bound-constrained Optimization )

Citation: Mathematics of Computation, 87 (2018), pp. 1327-1351.

Download: [PDF]

Entry Submitted: 08/16/2016
Entry Accepted: 08/16/2016
Entry Last Modified: 02/20/2018

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