A New Trust Region Algorithm With Conic Model

The new trust region subproblem with conic model proposed in 2005 cancelled the restrict on the level vector. A new feasible set of the subproblem was given. At the same time, the subproblem was divided into three different cases and three trust region subproblems with new conic model were established. The purpose of this paper is to give a new algorithm which is base on the trust region subproblem with new conic model for solving unconstrained optimization problem. First, three different cases were delt with respectively. For the first case, some literature had proved that it can be turned into the subproblem with quadratic model. For the other two cases, after some modification they are turned into the subproblems with quadratic model. Thus, all the cases are turned into the subproblems with quadratic model and the original subproblem can be easily solved. Then the paper gives a trust region algorithm with new conic model for solving the unconstrained optimization problems and its global convergence is proved. Last, the numerical experiment results are given in this paper. The numerical experiment results include the comparison of different algorithms and the comparison of quadratic model and conic model. The theoretical results and numerical experiments show that the trust region algorithm with new conic model is efficient and promising.