We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems lie on a manifold of approximately very low rank as a function of their controlling parameters (trust-region radius or regularization weight). Based on this, we build a … Read more
Motivated by encouraging numerical results in the literature, in this note we consider two specific variants of the trust-region subproblem and provide exact semidefinite representable reformulations. The first is over the intersection of two balls; the second is over the intersection of a ball and a special second-order conic representable set. Different from the technique … Read more
Semidefinite programming (SDP) problems typically utilize the constraint that X-xx’ is PSD to obtain a convex relaxation of the condition X=xx’, where x is an n-vector. In this paper we consider a new hyperplane branching method for SDP based on using an eigenvector of X-xx’. This branching technique is related to previous work of Saxeena, … Read more