Study On Some Problems About Line Search

This dissertation is devoted to some line search methods about nonlinear programming with a view to the current background of line search technique in China and in the world, which are mainly based on the master of the basic methods and theory of the linear search. Moreover, the main work of this dissertation can be summarized as follows:1. Some basic concepts, methods and theory about line search are introduced first which mainly prepares for the following research work. The current research background of line search technique in China and in the world is briefly summarized in this dissertation.2. Based on the analysis for several kinds of line search methods, a new line search algorithm for unconstrained optimization is proposed. It obtains the step-length after doing finite operations and has the same theoretical characters as the famous Wolf-Powell method for the minimization of the functions which are twice continuously differentiable and bounded below. Moreover, it requires two gradient evaluations at most in each of iteration and can save computation cost for the case when gradient evaluations are expensive. Numerical experiments show that the new algorithm in this paper is feasible and efficient.3. line search process is one basic part in all kinds of deterministic optimization methods which takes 80-90 percent of computing time to solve optimization problems. To provide a guide for the relative researchers who will use these methods, we selected several classical and effective methods for analyzing and evaluating.4. The global optimization of the Lennard-Jones clusters problem is a very simple yet reasonable accurate mathematical model of a real physical system. The global minimum of the L-J model can be used to interpreting the molecular conformation problem. The study about it is helpful in solving the protein folding problem. Considering the disadvantages of the modified algorithm, a hybrid descent method, combining the simulated annealing algorithm with the Hooke-Jeeves method, is proposed. The hybrid descent method reduces the computing time and enhances the rate of success.