Antonio M. Sudoso

Beyond binarity: Semidefinite programming for ternary quadratic problems

  • Frank de Meijer
  • Veronica Piccialli
  • Renata Sotirov
  • Antonio M. Sudoso
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming, Semi-definite Programming Tags , , ,

    We study the ternary quadratic problem (TQP), a quadratic optimization problem with linear constraints where the variables take values in {0,±1}. While semidefinite programming (SDP) techniques are well established for {0,1}- and {±1}-valued quadratic problems, no dedicated integer semidefinite programming framework exists for the ternary case. In this paper, we introduce a ternary SDP formulation … Read more

    SOS-SDP: an Exact Solver for Minimum Sum-of-Squares Clustering

  • Veronica Piccialli
  • Antonio M. Sudoso
  • Angelika Wiegele
    • Categories 0-1 Programming, Quadratic Programming, Semi-definite Programming

    The minimum sum-of-squares clustering problem (MSSC) consists in partitioning n observations into k clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. In this paper, we propose an exact algorithm for the MSSC problem based on the branch-and-bound technique. The lower bound is computed by … Read more