Some Further Studies And Applications Of IMPBOT Method

In recent years, ODE-type method attracts many attentions of experts and scholars widely. ODE-type method transforms the optimization problem into an ordinary differential equation-s(ODE system) problems, and then finds the extreme value point along the curve of the objective function. Among all ODE-based methods, the most successful algorithm is IMPBOT method in numerical test. By means of extensive numerical experiments, it can compare favorably with conventional Newton and Quasi-Newton algorithms as regards reliability, accuracy and efficiency, especially for highly nonlinear minimization problems-with narrow and curving valleys. Howev-er, IMPBOT method has to write Hessian matrix and may be solve linear equations system for many times. So it might brings a large of difficulties in implementation of the algorithm.As words above, this paper does some studies on IMPBOT method. The mainly meaning is as follows.The chapter2proposes a simple amendment for solving unconstrained optimization prob-lems. It obtains a trial step only by solving a linear equation system in each iteration. If the trial step cannot be accepted, the algorithm acquires the next iterative point along the direction of the trial step, in which the step is determined by a fixed formula. In this way, we not only avoid resolving the linear equation system repeatedly to obtain an acceptable trial step, but also reduce the amount of calculation without performing line search. Lastly, preliminary numerical results indieate that the new algorithms are workable and effective. The chapter3proposes an application for solving constrained optimization problems.