On The Methods For Unconstrained Optimization Problems And Their Realizes

In this paper, we study two types of practical algorithm for unconstrained optimization problem. We focus on a kind of improved subspace search algotithm and an improved hybrid optimization algorithm.In chapter of subspace search algotithm, the paper presents a new strategy---subspace search methods for unconstrained optimization problems. And the two dimensional subspace search strategy is applied in steepest descent algorithm, FR conjugate gradient algorithm and PRP conjugate gradient algorithm. Compared with the same algorithms under the line search strategy, the paper analyses their respective and superiority. Numerical results show that two dimensional search algorithm is feasible and effectiveness. Furthermore, from the view of practical application, the paper analyses subspace search algorithm and several effective line search algorithm. And from the analysis of the result, the new dimensional subspace search strategy improves the computation efficiency of the algorithm and save a large amount of the computation cost.In chapter of improved hybrid optimization algorithm, this paper proposes an improved hybrid optimization method for unconstrained optimization. The basic idea of improved hybrid optimization method lie in: firstly, the algorithm start iteration with the steepest descent method and find a good initial point on a large scale to modified Newton method; secondly, the algorithm start iteration with modified Newton method near the optimal point.The new method not only can make up the defect of Newton method that requires convex objective function but also possesses global convergence and locally quadratic convergence property under some conditions. Numerical experiments show that the new algorithm is efficient and reasonable.