An Iterative Algorithm for the Conic Trust Region Subproblem

Abstract

In Salahi (Optim Lett, 2016), using a variant of S-Lemma, an SOCP/SDP formulation is given for the conic trust region subproblem. Howeve, since currently SOCP/SDP formulation is not applicable for large scale problems, in this paper we present a generalized Newton algorithm for the problem using the parametrization approach of Dinkelbach. On several examples the new method and SOCP/SDP formulation are compared showing that the new method is extremely faster and moreover it is applicable for large scale instances.