Extended trust region subproblem

Extended trust region subproblem has been the focus of several recent research. It is the trust region subproblem with several additional linear inequalities. In this paper, first we review some existing results on trust region and extended subproblems. Then discuss their exact semidefinite relaxation. Finally, we present an efficient algorithm to solve the extended subproblem when the linear inequalities do not intersect inside the ball.