numerical experiments

Augmented Lagrangian methods under the Constant Positive Linear Dependence constraint qualification

  • Roberto Andreani
  • Ernesto G. Birgin
  • José Mario Martínez
  • María Laura Schuverdt
    • Categories Nonlinear Optimization Tags , , ,

    Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under … Read more

    Preprocessing sparse semidefinite programs via matrix completion

  • Katsuki Fujisawa
  • Mituhiro Fukuda
  • Kazuhide Nakata
    • Categories Semi-definite Programming Tags , , , , ,

    Considering that preprocessing is an important phase in linear programming, it should be systematically more incorporated in semidefinite programming solvers. The conversion method proposed by the authors (SIAM Journal on Optimization, vol.~11, pp.~647–674, 2000, and Mathematical Programming, Series B, vol.~95, pp.~303–327, 2003) is a preprocessing of sparse semidefinite programs based on matrix completion. This article … Read more

    PHoM – a Polyhedral Homotopy Continuation Method for Polynomial Systems

  • Katsuki Fujisawa
  • Sunyoung Kim
  • Masakazu Kojima
  • Tomohiko Mizutani
  • Takayuki Gunji
  • Akiko Takeda
    • Categories Nonlinear Systems and Least-Squares Tags , , , ,

    PHoM is a software package in C++ for finding all isolated solutions of polynomial systems using a polyhedral homotopy continuation method. Among three modules constituting the package, the first module StartSystem constructs a family of polyhedral-linear homotopy functions, based on the polyhedral homotopy theory, from input data for a given system of polynomial equations $\f(\x) … Read more