A Class Of Numerical Methods For Conic Trust Region Subproblems

Trust region method is a class of important optimization methods. This paper mainly discusses the conic trust region subproblem which is a key problem in conic trust region method. There are five chapters in this paper. The first chapter introduces the trust region method , quadratic model and conic model. This paper mainly studies the second case of a class of trust region subproblems involving conic model. And through the transformation, the conic trust region subproblem is converted into the problem of minimizing a quadratic function with two convex constraints. In the second chapter, this problem is converted into a dual problem, i.e. unconstrained maximization problem. We develop and prove some basic theorems and properties of this dual problem. In the third chapter, a modified Newton method is proposed for solving the dual problem. We prove general convergence and local convergence of this algorithm. At last we show the validity of the algorithm by using several numerical tests.