cubic optimization

Continuous Cubic Formulations for Cluster Detection Problems in Networks

  • Vladimir Boginski
  • Austin Buchanan
  • Sergiy Butenko
  • Vladimir Stozhkov
    • Categories Combinatorial Optimization, Global Optimization, Integer Programming Tags , , , , , ,

    The celebrated Motzkin-Straus formulation for the maximum clique problem provides a nontrivial characterization of the clique number of a graph in terms of the maximum value of a nonconvex quadratic function over a standard simplex. It was originally developed as a way of proving Tur\'{a}n’s theorem in graph theory, but was later used to develop … Read more

    On a Frank-Wolfe Type Theorem in Cubic Optimization

  • Diethard Klatte
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Quadratic Programming Tags , , , ,

    A classical result due to Frank and Wolfe (1956) says that a quadratic function $f$ attains its supremum on a nonempty polyhedron $M$ if $f$ is bounded from above on $M$. In this note, we present a stringent proof of the extension of this result to cubic optimization (known from Andronov, Belousov and Shironin (1982)). … Read more