inexact linear system solvers

A Note on the Implementation of an Interior-Point Algorithm for Nonlinear Optimization with Inexact Step Computations

  • Frank E. Curtis
  • Johannes Huber
  • Olaf Schenk
    • Categories Constrained Nonlinear Optimization Tags , , , , , , ,

    This paper describes an implementation of an interior-point algorithm for large-scale nonlinear optimization. It is based on the algorithm proposed by Curtis et al. (SIAM J Sci Comput 32:3447–3475, 2010), a method that possesses global convergence guarantees to first-order stationary points with the novel feature that inexact search direction calculations are allowed in order to … Read more

    An Interior-Point Algorithm for Large-Scale Nonlinear Optimization with Inexact Step Computations

  • Frank E. Curtis
  • Olaf Schenk
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs Tags , , , , , ,

    We present a line-search algorithm for large-scale continuous optimization. The algorithm is matrix-free in that it does not require the factorization of derivative matrices. Instead, it uses iterative linear system solvers. Inexact step computations are supported in order to save computational expense during each iteration. The algorithm is an interior-point approach derived from an inexact … Read more

    A Matrix-free Algorithm for Equality Constrained Optimization Problems with Rank-deficient Jacobians

  • Frank E. Curtis
  • Jorge Nocedal
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization, Infinite Dimensional Optimization Tags , , , , ,

    We present a line search algorithm for large-scale constrained optimization that is robust and efficient even for problems with (nearly) rank-deficient Jacobian matrices. The method is matrix-free (i.e., it does not require explicit storage or factorizations of derivative matrices), allows for inexact step computations, and is applicable for nonconvex problems. The main components of the … Read more

    An Inexact Newton Method for Nonconvex Equality Constrained Optimization

  • Richard H. Byrd
  • Frank E. Curtis
  • Jorge Nocedal
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351–369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the … Read more

    An Inexact SQP Method for Equality Constrained Optimization

  • Richard H. Byrd
  • Frank E. Curtis
  • Jorge Nocedal
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    We present an algorithm for large-scale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for large-scale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved … Read more