A Trust Region Algorithm Using Curve-Linear Searching Direction for Unconstrained Optimization

In the paper, aimed at the shortcoming of trust region method, we proposed a algorithm using negative curvature direction as its searching direction. The convergence of the algorithm was given. Furthermore, combing trust region method and curve-linear searching techniques, a trust region algorithm, using general curvelinear searching direction, was 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 that has the properties of curve-linear searching method and the global convergence of trust region method. Finally, we indicate that some searching directions of common methods can be as a special searching direction of the general method.