Gabriele Eichfelder

Erratum to: On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets” [Optim. Letters, 2012]

  • Peter J.C. Dickinson
  • Gabriele Eichfelder
  • Janez Povh
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    In this paper, an erratum is provided to the article “\emph{On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets}”, published in Optim.\ Letters, 2012. Due to precise observation of the first author, it has been found that the proof of Lemma 9 has a nontrivial gap, and consequently the main result (Theorem … Read more

    On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets

  • Gabriele Eichfelder
  • Janez Povh
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Quadratic Programming Tags , , ,

    In the paper we prove that any nonconvex quadratic problem over some set $K\subset \mathbb{R}^n$ with additional linear and binary constraints can be rewritten as linear problem over the cone, dual to the cone of K-semidefinite matrices. We show that when K is defined by one quadratic constraint or by one concave quadratic constraint and … Read more

    On reformulations of nonconvex quadratic programs over convex cones by set-semidefinite constraints

  • Gabriele Eichfelder
  • Janez Povh
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming

    The well-known result stating that any non-convex quadratic problem over the nonnegative orthant with some additional linear and binary constraints can be rewritten as linear problem over the cone of completely positive matrices (Burer, 2009) is generalized by replacing the nonnegative orthant with an arbitrary closed convex cone. This set-semidefinite representation result implies new semidefinite … Read more

    Copositivity detection by difference-of-convex decomposition and omega-subdivision

  • Immanuel M. Bomze
  • Gabriele Eichfelder
    • Categories Linear, Cone and Semidefinite Programming Tags

    We present three new copositivity tests based upon difference-of-convex (d.c.) decompositions, and combine them to a branch-and-bound algorithm of $\omega$-subdivision type. The tests employ LP or convex QP techniques, but also can be used heuristically using appropriate test points. We also discuss the selection of efficient d.c.~decompositions and propose some preprocessing ideas based on the … Read more