doubly nonnegative matrices

Moment approximations for set-semidefinite polynomials

  • Peter J.C. Dickinson
  • Janez Povh
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    The set of polynomials which are nonnegative over a subset of the nonnegative orthant (we call them set semidefinite) have many uses in optimization. A common example of this type of set is the set of copositive matrices, where effectively we are considering nonnegativity over the entire nonnegative orthant and we limit the polynomials to … Read more

    The Difference Between 5×5 Doubly Nonnegative and Completely Positive Matrices

  • Kurt M. Anstreicher
  • Samuel Burer
  • Mirjam Duer
    • Categories Convex Optimization, Global Optimization Theory, Semi-definite Programming Tags , ,

    The convex cone of $n \times n$ completely positive (CPP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CPP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that, for $n \le 4$ only, every DNN matrix is CPP. … Read more