A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
A local convergence theory for combined inexact-Newton/finite-difference projection methods
SIAM Journal on Numerical Analysis
Global convergence and stabilization of unconstrained minimization methods without derivatives
Journal of Optimization Theory and Applications
Nonmonotone stabilization methods for nonlinear equations
Journal of Optimization Theory and Applications
NITSOL: A Newton Iterative Solver for Nonlinear Systems
SIAM Journal on Scientific Computing
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
On the Global Convergence of Derivative-Free Methods for Unconstrained Optimization
SIAM Journal on Optimization
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
SIAM Journal on Optimization
Nonmonotone Globalization Techniques for the Barzilai-Borwein Gradient Method
Computational Optimization and Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
A projected conjugate gradient method for compressive sensing
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
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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.