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
SIAM Journal on Numerical Analysis
Nonmonotonic trust region algorithm
Journal of Optimization Theory and Applications
Nonmonotone line search for minimax problems
Journal of Optimization Theory and Applications
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
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
SIAM Journal on Optimization
Convergence of nonmonotone line search method
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Incorporating nonmonotone strategies into the trust region method for unconstrained optimization
Computers & Mathematics with Applications
A new nonmonotone line search technique for unconstrained optimization
Journal of Computational and Applied Mathematics
Global convergence of the nonmonotone MBFGS method for nonconvex unconstrained minimization
Journal of Computational and Applied Mathematics
A new family of conjugate gradient methods
Journal of Computational and Applied Mathematics
A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems
Optimization Methods & Software
A globally convergent BFGS method with nonmonotone line search for non-convex minimization
Journal of Computational and Applied Mathematics
Hybrid spectral gradient method for the unconstrained minimization problem
Journal of Global Optimization
A new nonmonotone trust-region method of conic model for solving unconstrained optimization
Journal of Computational and Applied Mathematics
A Non-monotone Line Search Algorithm for Unconstrained Optimization
Journal of Scientific Computing
Notes on the Dai-Yuan-Yuan modified spectral gradient method
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Modified nonmonotone Armijo line search for descent method
Numerical Algorithms
Journal of Computational and Applied Mathematics
Preconditioning non-monotone gradient methods for retrieval of seismic reflection signals
Advances in Computational Mathematics
An efficient nonmonotone trust-region method for unconstrained optimization
Numerical Algorithms
Computational Optimization and Applications
A nonmonotone PSB algorithm for solving unconstrained optimization
Computational Optimization and Applications
A modified ODE-based algorithm for unconstrained optimization problems
Numerical Algorithms
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The technique of nonmonotone line search has received many successful applications and extensions in nonlinear optimization. This paper provides some basic analyses of the nonmonotone line search. Specifically, we analyze the nonmonotone line search methods for general nonconvex functions along different lines. The analyses are helpful in establishing the global convergence of a nonmonotone line search method under weaker conditions on the search direction. We explore also the relations between nonmonotone line search and R-linear convergence assuming that the objective function is uniformly convex. In addition, by taking the inexact Newton method as an example, we observe a numerical drawback of the original nonmonotone line search and suggest a standard Armijo line search when the nonmonotone line search condition is not satisfied by the prior trial steplength. The numerical results show the usefulness of such suggestion for the inexact Newton method.