A Non-Monotone Tensor Method for Unconstrained Optimization Problems
نویسندگان
چکیده
The tensor method for unconstrained optimization was first introduced by Schnable and Chow [SIAM Journal on Optimization, 1 (1991): 293–315], where each iteration bases upon a fourth order model for the objective function. In this paper, we propose a tensor method with a non-monotone line search scheme for solving the unconstrained optimization problem, and show the convergence of the method. We evaluate the proposed method by several numerical examples, and compare the obtained numerical results with those by the modified Newton method, the tensor method, and the monotone tensor method. Through the numerical results, we can see that the new method is more effective than others for the problems we tested. Key–Words: unconstrained optimization, non-monotone linear search, non-monotone tensor method. AMS subject classifications 90C30, 65K05.
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