moment cone relaxation

Lagrangian-Conic Relaxations, Part II: Applications to Polynomial Optimization Problems

  • Naohiko Arima
  • Sunyoung Kim
  • Masakazu Kojima
  • Kim-Chuan Toh
    • Categories Convex Optimization, Semi-definite Programming Tags , , , ,

    We present the moment cone (MC) relaxation and a hierarchy of sparse Lagrangian-SDP relaxations of polynomial optimization problems (POPs) using the unified framework established in Part I. The MC relaxation is derived for a POP of minimizing a polynomial subject to a nonconvex cone constraint and polynomial equality constraints. It is an extension of the … Read more

    Extension of Completely Positive Cone Relaxation to Polynomial Optimization

  • Naohiko Arima
  • Sunyoung Kim
  • Masakazu Kojima
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    We propose the moment cone relaxation for a class of polynomial optimization problems (POPs) to extend the results on the completely positive cone programming relaxation for the quadratic optimization (QOP) model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the POPs, so that efficient numerical methods … Read more