Luca Bergamaschi

A New Preconditioning Approach for an Interior Point-Proximal Method of Multipliers for Linear and Convex Quadratic Programming

  • Luca Bergamaschi
  • Jacek Gondzio
  • John W. Pearson
  • Ángeles Martínez
  • Spyridon Pougkakiotis
    • Categories Convex Optimization, Linear Programming, Quadratic Programming Tags , , , ,

    In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers, which in turn results in a primal-dual regularized interior point method. Application of this method gives rise to a … Read more

    BFGS-like updates of constraint preconditioners for sequences of KKT linear systems

  • Luca Bergamaschi
  • Valentina De Simone
  • Daniela di Serafino
  • Angeles Martinez
    • Categories Nonlinear Optimization, Quadratic Programming Tags

    We focus on efficient preconditioning techniques for sequences of KKT linear systems arising from the interior point solution of large convex quadratic programming problems. Constraint Preconditioners (CPs), though very effective in accelerating Krylov methods in the solution of KKT systems, have a very high computational cost in some instances, because their factorization may be the … Read more