Approximate norm descent methods for constrained nonlinear systems. (English) Zbl 1383.65051

Summary: 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.


65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
90C25 Convex programming
90C53 Methods of quasi-Newton type
90C56 Derivative-free methods and methods using generalized derivatives


STRSCNE; levmar
Full Text: DOI


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