A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
A truncated Newton method with nonmonotone line search for unconstrained optimization
Journal of Optimization Theory and Applications
Avoiding the Maratos effect by means of a nonmonotone line search I. general constrained problems
SIAM Journal on Numerical Analysis
Nonmonotonic trust region algorithm
Journal of Optimization Theory and Applications
CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
An assessment of nonmonotone linesearch techniques for unconstrained optimization
SIAM Journal on Scientific Computing
Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints
Mathematical Programming: Series A and B
Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
Some convergence properties of descent methods
Journal of Optimization Theory and Applications
A class of gradient unconstrained minimization algorithms with adaptive stepsize
Journal of Computational and Applied Mathematics
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
SIAM Journal on Optimization
On the nonmonotone line search
Journal of Optimization Theory and Applications
Relaxed Steepest Descent and Cauchy-Barzilai-Borwein Method
Computational Optimization and Applications
Global convergence of nonmonotone descent methods for unconstrained optimization problems
Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization
ACM Transactions on Mathematical Software (TOMS)
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Convergence of nonmonotone line search method
Journal of Computational and Applied Mathematics
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Nonmonotone line search approach is a new technique for solving optimization problems. It relaxes the line search range and finds a larger step-size at each iteration, so as to possibly avoid local minimizer and run away from narrow curved valley. It is helpful to find the global minimizer of optimization problems. In this paper we develop a new modification of matrix-free nonmonotone Armijo line search and analyze the global convergence and convergence rate of the resulting method. We also address several approaches to estimate the Lipschitz constant of the gradient of objective functions that would be used in line search algorithms. Numerical results show that this new modification of Armijo line search is efficient for solving large scale unconstrained optimization problems.