Richard H. Byrd

On the Convergence of Successive Linear-Quadratic Programming Algorithms

  • Richard H. Byrd
  • Nicholas I. M. Gould
  • Jorge Nocedal
  • Richard A. Waltz
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , ,

    The global convergence properties of a class of penalty methods for nonlinear programming are analyzed. These methods include successive linear programming approaches, and more specifically, the successive linear-quadratic programming approach presented by Byrd, Gould, Nocedal and Waltz (Math. Programming 100(1):27–48, 2004). Every iteration requires the solution of two trust-region subproblems involving piecewise linear and quadratic … Read more

    On the Convergence of Successive Linear Programming Algorithms

  • Richard H. Byrd
  • Nicholas I. M. Gould
  • Jorge Nocedal
  • Richard A. Waltz
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    We analyze the global convergence properties of a class of penalty methods for nonlinear programming. These methods include successive linear programming approaches, and more specifically the SLP-EQP approach presented in \cite{ByrdGoulNoceWalt02}. Every iteration requires the solution of two trust region subproblems involving linear and quadratic models, respectively. The interaction between the trust regions of these … Read more

    An Active-Set Algorithm for Nonlinear Programming Using Linear Programming and Equality Constrained Subproblems

  • Richard H. Byrd
  • Nicholas I. M. Gould
  • Jorge Nocedal
  • Richard A. Waltz
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark Tags , , , , ,

    This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained … Read more

    On the Convergence of Newton Iterations to Non-Stationary Points

  • Richard H. Byrd
  • Marcelo Marazzi
  • Jorge Nocedal
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , ,

    We study conditions under which line search Newton methods for nonlinear systems of equations and optimization fail due to the presence of singular non-stationary points. These points are not solutions of the problem and are characterized by the fact that Jacobian or Hessian matrices are singular. It is shown that, for systems of nonlinear equations, … Read more

    Feasible Interior Methods Using Slacks for Nonlinear Optimization

  • Richard H. Byrd
  • Richard A. Waltz
  • Jorge Nocedal
    • Categories Constrained Nonlinear Optimization Tags , , , , , , , ,

    A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the … Read more