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
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Avoiding the Maratos effect by means of a nonmonotone line search I. general constrained problems
SIAM Journal on Numerical Analysis
On the nonmonotone line search
Journal of Optimization Theory and Applications
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
SIAM Journal on Optimization
Scaled conjugate gradient algorithms for unconstrained optimization
Computational Optimization and Applications
A smoothing-type algorithm for solving system of inequalities
Journal of Computational and Applied Mathematics
A nonmonotone smoothing-type algorithm for solving a system of equalities and inequalities
Journal of Computational and Applied Mathematics
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The monotone line search schemes have been extensively used in the iterative methods for solving various optimization problems. It is well known that the non-monotone line search technique can improve the likelihood of finding a global optimal solution and the numerical performance of the methods, especially for some difficult nonlinear problems. The traditional non-monotone line search approach requires that a maximum of recent function values decreases. In this paper, we propose a new line search scheme which requires that a convex combination of recent function values decreases. We apply the new line search technique to solve unconstrained optimization problems, and show the proposed algorithm possesses global convergence and R-linear convergence under suitable assumptions. We also report the numerical results of the proposed algorithm for solving almost all the unconstrained testing problems given in CUTEr, and give numerical comparisons of the proposed algorithm with two famous non-monotone methods.