In this paper we study nonmonotone globalization techniques, in connection with iterative derivative-free methods for solving a system of nonlinear equations in several variables. First we define and analyze a class of nonmonotone derivative-free linesearch techniques for unconstrained minimization of differentiable functions. Then we introduce a globalization scheme, which combines nonmonotone watchdog rules and nonmonotone linesearches, and we study the application of this scheme to some recent extensions of the Barzilai-Borwein gradient method and to hybrid stabilization algorithms employing linesearches along coordinate directions. Numerical results on a set of standard test problems show that the proposed techniques can be of value in the solution of large-dimensional systems of equations.

Nonmonotone derivative-free methods for nonlinear equations / Grippo, Luigi; Sciandrone, M.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - STAMPA. - 37:3(2007), pp. 297-328. [10.1007/s10589-007-9028-x]

Nonmonotone derivative-free methods for nonlinear equations

GRIPPO, Luigi;M. Sciandrone
2007

Abstract

In this paper we study nonmonotone globalization techniques, in connection with iterative derivative-free methods for solving a system of nonlinear equations in several variables. First we define and analyze a class of nonmonotone derivative-free linesearch techniques for unconstrained minimization of differentiable functions. Then we introduce a globalization scheme, which combines nonmonotone watchdog rules and nonmonotone linesearches, and we study the application of this scheme to some recent extensions of the Barzilai-Borwein gradient method and to hybrid stabilization algorithms employing linesearches along coordinate directions. Numerical results on a set of standard test problems show that the proposed techniques can be of value in the solution of large-dimensional systems of equations.
2007
barzilai-borwein method; derivative-free linesearch; hybrid methods; nonlinear equations; nonmonotone techniques
01 Pubblicazione su rivista::01a Articolo in rivista
Nonmonotone derivative-free methods for nonlinear equations / Grippo, Luigi; Sciandrone, M.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - STAMPA. - 37:3(2007), pp. 297-328. [10.1007/s10589-007-9028-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/809
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