Research Of Trust Region Methods Based New Conic Model For Unconstrained Optinrization Problem

The trust region algorithm is an effective numerical calculation method for solvingnonlinear optimization problems, especially for the unconstrained optimization problem.Nowadays, many researchers in nonlinear optimization area have focused on the trustregion method. In the traditional trust region mothed, the objection function can beapproximated by using the quadratic model. The conic model is the generalization ofquadratic models. Compared with the quadratic model, except for the convergence ofNewton’s method and the global convergence, the conic model with approximation ofthe objective function is better when we solve the strongly non-quadratic form and moredramatic change of curvature function.And the conic model can also access to moreinformation from the previous point. So more and more researchers have paid attentionto the trust region method. The trust region algorithm of new conic model is proposedby Ni-Qin in2005which has broken through the limitation of the trust region radius andthe horizontal vector. The new model opens up a broad space for the conic modeldevelopment.This paper addresses the trust region algorithm of new conic model for theunconstrained optimization problem. Details are summarized as follows:In the first chapter, the advancing and development of optimization problem,traditional trust region method, and the new trust region algorithm of conic model areintroduced.In the second chapter, combining the adaptive technology with the non-monotonetechnique which proposed by Zhang and Hager, traditional non-monotone trust regionalgorithm of new conic model is improved. The new algorithm can access to moreinformation from the previous point and compensate for the omission of the optionalpoint, which can improve efficiency of the algorithm. Finally, we prove the globalconvergence of the method.In the third chapter, based on the above method, the Masoud Ahookhosh’snon-monotone technical is introduced to avoid updating parameters kandQk. Then,the modified non-monotone adaptive trust region algorithm of a new conic model isinvestigated. The numerical experiment shows effectiveness of the method.In the forth chapter, on the basis of the non-monotone technique proposed by Moand Gu and adding the filter techniques at the same time, Non-monotonemultidimensional filter trust region of a new conic model is studied. The acceptable criterion of the iteration points is relaxed in new method.Under certain assumptions, theglobal convergence and the efficiency of the algorithm are proved.