A Class Of Methods Of Conic Interpolation Model For Unconstrained Optimization

This paper mainly concerns the conic interpolation model method for unconstrained optimization and its implementation, the structure of which is organized as follows:Firstly, we survey the history of the direct search methods concisely, and summarize the methods that are currently considered to be effective for unconstrained optimization. Secondly, the quadratic interpolation model method (QIM), which now is supported by profound theory and graceful test results, is discussed.In the third chapter, we explore the conic interpolation model (CIM), including its origin, improvement contrasted with QIM. Especially, we give the computing steps and convergent property of the method proposed by Ni and Hu, because our further research is based on this method. Meanwhile, we point out the privilege and defective of CIM.The fourth chapter is the main body of this paper. We explore how to apply the CIM to solve unconstrained optimization problems effectively. At first, on the basis of the sufficient and necessary optimality conditions, we give a certain algorithm to compute the trust region subproblem; then, we draw out a different scheme for parameter vector in CIM.In the last chapter, series of numerical experiments are made. The results show that conic interpolation model method is an efficient direct search method. This should be further researched.