A Trust Region Algorithm Based on General Curve-linear Searching Direction for Unconstrained Optimization

In this paper, aiming at the shortcoming of trust region method, we propose an algorithm using negative curvature direction as its searching direction. The convergence of the algorithm is given. Furthermore, combining trust region method and curve-linear searching techniques, using general curve-linear searching direction a trust region algorithm is proposed. We proved its efficiency and feasibility. The algorithm has adjustability and can select or update its searching direction according to the iteration. This allows the algorithm to have the properties of curve-linear searching method and the global convergence of trust region method. Finally, we indicated that some searching directions of common methods are a special searching direction of the general method.