Research On The Algorithms For Unconstrained Optimization

The optimized method is a young discipline with very strong utility. It mainly studies the optimized way and plan of each system by mathematical method, expresses the idea that actual problems are processed from the mathematical angle. Unconstrained optimization is an important branch in optimization and has become the focus that many scholars study. In the process of the actual problem's solution, unconstrained optimization has an important theory significance to make a study of.The thesis is divided into three chapters:Chapter 1 is the introduction, which mainly contains the general situation of optimization, the basic concept, some line search methods, several extensive descent methods for unconstrained optimization, and the article arrangement.In chapter 2, based on steepest descent method, BB gradient method and their hybrid method, a new alternate stepsize gradient method is proposed, and its convergence is proved theoretically. Numerical experiment shows that the method is feasible.In chapter 3, in light of the character of conjugate gradient method, a new descent method is proposed. The proof of the method's global convergence is given under Wolfe line search without the descent property. Numerical experiment shows that the method is efficient.