polynomial optimization problems

User Manual for BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems with Binary, Box and Complementarity Constraints

  • Naoki Ito
  • Sunyoung Kim
  • Masakazu Kojima
  • Kim-Chuan Toh
  • Akiko Takeda
    • Categories Convex Optimization, Global Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    BBCPOP proposed in [4] is a MATLAB implementation of a hierarchy of sparse doubly nonnegative (DNN) relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box and complementarity constraints. Given a POP in the class and a relaxation order (or a hierarchy level), BBCPOP constructs a simple conic optimization problem (COP), which … Read more

    A Facial Reduction Algorithm for Finding Sparse SOS Representations

  • Masakazu Muramatsu
  • Hayato Waki
    • Categories Convex Optimization, Global Optimization Theory, Semi-definite Programming Tags , , ,

    Facial reduction algorithm reduces the size of the positive semidefinite cone in SDP. The elimination method for a sparse SOS polynomial ([3]) removes unnecessary monomials for an SOS representation. In this paper, we establish a relationship between a facial reduction algorithm and the elimination method for a sparse SOS polynomial. Citation Technical Report CS-09-02, Department … Read more