A Conic Trust Region Method Based On New Horizontal Vector

The conic method was first proposed by Davidon in 1980. The conic model has more freedom. Firstly, the model can fully use the information in the previous iteration. Secondly, it can approximate the objective function better than a quadratic one when the function has strong non-quadratic behavior or its curvature changes severely. Di and Sun proposed the conic trust region method in 1996. After that, many researchers studied the construction of conic model and the solution of the subproblem.In the thesis we mainly discuss the choice of horizontal vector and the algorithm based on conic model which can solve the unconstrained optimization problems. The new horizontal vector is proposed from the aspect of high order model. Based on the new horizontal vector, a new conic trust region method is proposed. After that the global convergence is proved, and the numerical results are reported.The paper is organized as follows. The first chapter introduces the origins and progress in research of the conic trust region method for solving unconstrained optimization. The second chapter describes some basic knowledge of linear search method, trust region method and conic model. In the third chapter, the deduction of new horizontal vector is showed, and a conic trust region method based on the new horizontal vector is proposed. In the fourth chapter, the convergence is proved. In the fifth chapter, the numerical results are reported. Finally, the conclusion and some further problems are given.