complex polynomial optimization

A real moment-HSOS hierarchy for complex polynomial optimization with real coefficients

  • Jie Wang
  • Victor Magron
    • Categories Global Optimization, Global Optimization Theory, Semi-definite Programming Tags , , , ,

    This paper proposes a real moment-HSOS hierarchy for complex polynomial optimization problems with real coefficients. We show that this hierarchy provides the same sequence of lower bounds as the complex analogue, yet is much cheaper to solve. In addition, we prove that global optimality is achieved when the ranks of the moment matrix and certain … Read more

    A more efficient reformulation of complex SDP as real SDP

  • Jie Wang
    • Categories Global Optimization Theory, Semi-definite Programming Tags , , , ,

    This note proposes a novel reformulation of complex semidefinite programs (SDPs) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of complex polynomial optimization problems as real SDPs and derive some further reductions by exploiting structure of the complex SDP relaxations. Various numerical examples demonstrate that our new reformulation … Read more