decomposition

Gradient Projection Methods for Quadratic Programs and Applications in Training Support Vector Machines

  • Thomas Serafini
  • Luca Zanni
  • Gaetano Zanghirati
    • Categories Data-Mining, Quadratic Programming Tags , , , ,

    Gradient projection methods based on the Barzilai-Borwein spectral steplength choices are considered for quadratic programming problems with simple constraints. Well known nonmonotone spectral projected gradient methods and variable projection methods are discussed. For both approaches the behavior of different combinations of the two spectral steplengths is investigated. A nw adaptive stplength alternating rule is proposed, … Read more

    Self-scaled barrier functions on symmetric cones and their classification

  • Osman Guler
  • Raphael Hauser
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    Self-scaled barrier functions on self-scaled cones were introduced through a set of axioms in 1994 by Y.E. Nesterov and M.J. Todd as a tool for the construction of long-step interior point algorithms. This paper provides firm foundation for these objects by exhibiting their symmetry properties, their intimate ties with the symmetry groups of their domains … Read more