steepest descent methods

Handling Nonpositive Curvature in a Limited Memory Steepest Descent Method

  • Frank E. Curtis
  • Wei Guo
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    We propose a limited memory steepest descent (LMSD) method for solving unconstrained optimization problems. As a steepest descent method, the step computation in each iteration requires the evaluation of a gradient of the objective function and the calculation of a scalar step size only. When employed to solve certain convex problems, our method reduces to … Read more

    On spectral properties of steepest descent methods

  • Roberta De Asmundis
  • Daniela di Serafino
  • Gerardo Toraldo
  • Filippo Riccio
    • Categories Nonlinear Optimization, Quadratic Programming Tags , ,

    In recent years it has been made more and more clear that the critical issue in gradient methods is the choice of the step length, whereas using the gradient as search direction may lead to very effective algorithms, whose surprising behaviour has been only partially explained, mostly in terms of the spectrum of the Hessian … Read more