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.

Approximate norm descent methods for constrained nonlinear systems

Porcelli M.;
2018

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.
Morini B.; Porcelli M.; Toint P.L.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/711342
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