sum of squares

A Note on Sparse SOS and SDP Relaxations for Polynomial Optimization Problems over Symmetric Cones

  • Masakazu Kojima
  • Masakazu Muramatsu
    • Categories Constrained Nonlinear Optimization, Global Optimization, Semi-definite Programming Tags , , , , , ,

    This short note extends the sparse SOS (sum of squares) and SDP (semidefinite programming) relaxation proposed by Waki, Kim, Kojima and Muramatsu for normal POPs (polynomial optimization problems) to POPs over symmetric cones, and establishes its theoretical convergence based on the recent convergence result by Lasserre on the sparse SOS and SDP relaxation for normal … Read more

    An Extension of Sums of Squares Relaxations to Polynomial Optimization Problems over Symmetric Cones

  • Masakazu Kojima
  • Masakazu Muramatsu
    • Categories Global Optimization Theory, Semi-definite Programming Tags , , , , , ,

    This paper is based on a recent work by Kojima which extended sums of squares relaxations of polynomial optimization problems to polynomial semidefinite programs. Let ${\cal E}$ and ${\cal E}_+$ be a finite dimensional real vector space and a symmetric cone embedded in ${\cal E}$; examples of $\calE$ and $\calE_+$ include a pair of the … Read more