Direct Search Method Of Fractional Interplolation Model For Unconstrained Optimization

Direct search methods enjoyed great interest as researchers between1960s and1970s,because it has high demand from practitioners. Now, it is also high demand that makes theresearch on the direct search method revive．In the thesis we mainly discuss the algorithms and theory of direct search methods, especiallyof the direct search method based on separable fractional interpolation model. The structure of thispaper is organized as follows．The first chapter describes the origins and progress in research of direct search method forsolving unconstrained optimization. The second chapter describes some basic knowledge of thisarticle, the theoretical knowledge and algorithms of the trust region mothod, the mobile asymptotemethod and the direct search method of quadratic tridiagonal interpolation model. The thirdchapter describes the fractional interpolation model, based on this model a new direct searchalgorithm is proposed for solving unconstrained optimization problems. The convergence ofnew direct search algorithm is proved. In the chapter IV, numerical results of the direct searchmethods based on fractional interpolation and diagonal interpolation are reported andcompared. Finally, this conclusion is given.