Quasi-Newton Trust Region Methods Based On The Conic Model

Traditional trust region methods are based on a quadratic model. Conic model proposed by Davidon can take into account more information from previous iterations than quadratic model. In this paper, we mainly discuss the modified quasi-Newton trust region methods based on a conic model (TRCM method) and prove their convergence properties. In the first chapter, the history of the trust region method based on quadratic model is introduced. Then, we give the properties of a conic model and introduce TRCM methods. We propose two modified TRCM methods in the second chapter. The third chapter is the key part of this paper. We propose the new interpolation conditions and establish another new TRCM method. In the fourth chapter, we propose a new algorithm for solving the subproblem of TRCM method. In the fifth chapter, we describe the three new TRCM methods and give their global convergence . In the sixth chapter, we prove the local linear and Q-superlinear convergence of the modified TRCM methods. In the last, we give numerical results of the three modified TRCM methods. The numerical results show that the modified TRCM methods are efficient.