Trust region subproblem

A Note on Semidefinite Representable Reformulations for Two Variants of the Trust-Region Subproblem

  • Sarah Kelly
  • Yuyuan Ouyang
  • Boshi Yang
    • Categories Cone Programming, Semi-definite Programming Tags , , ,

    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

    Solving Two-Trust-Region Subproblems using Semidefinite Optimization with Eigenvector Branching

  • Kurt M. Anstreicher
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Semi-definite Programming Tags , , , ,

    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