Document Type : Original Article

Author

Department of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

Abstract

In this paper, we present a new trust region method for unconstrained optimization problems with locally Lipschitz continuous, nonconvex functions. In this method, in the ratio test, the current objective function value is replaced with maximum of some objective function values in the previous iterations. The new method nonmonotone properties and prevents falling into narrow valleys. Proving global convergence requires only two conditions: 1- there should be is a sufficient reduction for the approximate model in the solution of trust region subproblem, 2- the approximation Hessian matrix be bounded. Then, the convergence property of this method is investigated. Finally, the presented method is implemented on some nonconvex problems in MATLAB environment and numerical results are compared with the nonsmooth trust region method.

Keywords

Main Subjects

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