Approximate norm descent methods for constrained nonlinear systems
Benedetta Morini (benedetta.moriniunifi.it)
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.
Entry Submitted: 08/16/2016
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