An ODE-based trust region method for unconstrained optimization problems

Authors:
Yigui Ou;Qian Zhou;Haichan Lin
Affiliations:
Department of Mathematics, Hainan University, Haikou 570228, China;Department of Mathematics, Hainan University, Haikou 570228, China;Department of Mathematics, Hainan University, Haikou 570228, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, a new trust region algorithm is proposed for solving unconstrained optimization problems. This method can be regarded as a combination of trust region technique, fixed step-length and ODE-based methods. A feature of this proposed method is that at each iteration, only a system of linear equations is solved to obtain a trial step. Another is that when a trial step is not accepted, the method generates an iterative point whose step-length is defined by a formula. Under some standard assumptions, it is proven that the algorithm is globally convergent and locally superlinear convergent. Preliminary numerical results are reported.