Study On Convergence Analysis Of Some Optimization Methods And Applications

Optimization is an important component of operations research, which has been applied to practical problems hi many scientific and engineering disciplines. This paper is devoted to some numerical optimization methods and optimization models for solving practical problems in real world. The methods we concern with are the conjugate gradient algorithms, evolutionary algorithms and goal programming. The main work of the paper can be summarized as follows:1. A mixed HS-FR conjugate gradient algorithm is proposed. Two convergence theorems without the sufficient descent condition for the mixed HS-FR algorithm are given. The convergence theorem of a class of conjugate gradient algorithms is proven, which extend the main convergence theorem in Gilbert and Noceda (1992).2. Evolution strategy procedures for real-valued function optimization for the purpose of analyzing its asymptotic convergence properties are described. Two convergence theorems, which show that under suitable conditions evolution strategy asymptotically converges to a global minimum point with probability one, are given. A mixed EP-ES evolutionary algorithm for real-valued function optimization is proposed. Numerical results illustrate that the proposed algorithm is efficient.3. According to the demands of making the medium- and long-term highway networks planning in certain province, a goal-programming model for arterial highway network grade structure optimization is established, and an algorithm with example is given.