linear algebra

Minimizing convex quadratics with variable precision Krylov methods

  • Serge Gratton
  • Philippe L. Toint
  • Ehouarn Simon
    • Categories Convex Optimization, Optimization Software and Modeling Systems, Quadratic Programming Tags , ,

    Iterative algorithms for the solution of convex quadratic optimization problems are investigated, which exploit inaccurate matrix-vector products. Theoretical bounds on the performance of a Conjugate Gradients and a Full-Orthormalization methods are derived, the necessary quantities occurring in the theoretical bounds estimated and new practical algorithms derived. Numerical experiments suggest that the new methods have significant … Read more

    Interior point methods for massive support vector machines

  • Michael C. Ferris
  • Todd S. Munson
    • Categories Data-Mining Tags , ,

    We investigate the use of interior point methods for solving quadratic programming problems with a small number of linear constraints where the quadratic term consists of a low-rank update to a positive semi-definite matrix. Several formulations of the support vector machine fit into this category. An interesting feature of these particular problems is the volume … Read more