completely positive program

Unifying semidefinite and set-copositive relaxations of binary problems and randomization techniques

  • Florian Jarre
  • Felix Lieder
  • Fatameh Bani Asadi Rad
    • Categories 0-1 Programming, Combinatorial Optimization Tags , , , , , ,

    A reformulation of quadratically constrained binary programs as duals of set-copositive linear optimization problems is derived using either \(\{0,1\}\)-formulations or \(\{-1,1\}\)-formulations. The latter representation allows an extension of the randomization technique by Goemans and Williamson. An application to the max-clique problem shows that the max-clique problem is equivalent to a linear program over the max-cut … Read more

    Burer’s Key Assumption for Semidefinite and Doubly Nonnegative Relaxations

  • Florian Jarre
    • Categories Approximation Algorithms, Quadratic Programming, Semi-definite Programming Tags , ,

    Burer has shown that completely positive relaxations of nonconvex quadratic programs with nonnegative and binary variables are exact when the binary variables satisfy a so-called key assumption. Here we show that introducing binary variables to obtain an equivalent problem that satisfies the key assumption will not improve the semidefinite relaxation, and only marginally improve the … Read more