An Algorithm For Solving Conic Model Nonconvex Trust-region Subproblem

In this paper, we consider a nonconvex conic model trust-region subproblem, and develop a method for solving this subproblem and discuss the convergence theory of the method. The new conic model trust-region subproblem was proposed in 2005, and divided into three different cases. The first two cases can be converted into quadratic model or convex programming problem with quadratic constraint, but the third one is a nonconvex programming problem. We analyze it theoretically, and convert it into two convex programming problems. Moreover, we give some dual properties of these problems, and on this basis, we present a dual algorithm for solving the nonconvex conic model trust-region subproblem. In addition, we prove globe convergence of it and obtain a local result, the rate of convergence is Q-superlinear. Some numerical results are also given to illustrate the efficiency of the algorithm.