A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Mathematical Programming: Series A and B
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Global convergence of a two-parameter family of conjugate gradient methods without line search
Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
Combination trust-region line-search methods for unconstrained optimization
Combination trust-region line-search methods for unconstrained optimization
A nonmonotone trust-region method of conic model for unconstrained optimization
Journal of Computational and Applied Mathematics
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In this paper, we present a nonmonotone conic trust region method based on line search technique for unconstrained optimization. The new algorithm can be regarded as a combination of nonmonotone technique, line search technique and conic trust region method. When a trial step is not accepted, the method does not resolve the trust region subproblem but generates an iterative point whose steplength satisfies some line search condition. The function value can only be allowed to increase when trial steps are not accepted in close succession of iterations. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the existing methods.