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
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)
Trust-region methods
On the nonmonotone line search
Journal of Optimization Theory and Applications
A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
SIAM Journal on Optimization
Journal of Computational and Applied Mathematics
A Nonmonotone trust region method with adaptive radius for unconstrained optimization problems
Computers & Mathematics with Applications
Computational Optimization and Applications
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The monotone trust-region methods are well-known techniques for solving unconstrained optimization problems. While it is known that the nonmonotone strategies not only can improve the likelihood of finding the global optimum but also can improve the numerical performance of approaches, the traditional nonmonotone strategy contains some disadvantages. In order to overcome to these drawbacks, we introduce a variant nonmonotone strategy and incorporate it into trust-region framework to construct more reliable approach. The new nonmonotone strategy is a convex combination of the maximum of function value of some prior successful iterates and the current function value. It is proved that the proposed algorithm possesses global convergence to first-order and second-order stationary points under some classical assumptions. Preliminary numerical experiments indicate that the new approach is considerably promising for solving unconstrained optimization problems.