large-scale nonlinear programming

A Brief History of Filter Methods

  • Roger Fletcher
  • Sven Leyffer
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    We consider the question of global convergence of iterative methods for nonlinear programming problems. Traditionally, penalty functions have been used to enforce global convergence. In this paper we review a recent alternative, so-called filter methods. Instead of combing the objective and constraint violation into a single function, filter methods view nonlinear optimization as a biobjective … Read more

    Iterative Solution of Augmented Systems Arising in Interior Methods

  • Anders Forsgren
  • Philip E. Gill
  • Joshua D. Griffin
    • Categories Constrained Nonlinear Optimization Tags , , , , , , ,

    Iterative methods are proposed for certain augmented systems of linear equations that arise in interior methods for general nonlinear optimization. Interior methods define a sequence of KKT equations that represent the symmetrized (but indefinite) equations associated with Newton’s method for a point satisfying the perturbed optimality conditions. These equations involve both the primal and dual … Read more