krylov subspace methods

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

    Subspace trust-region methods for large bound-constrained nonlinear equations

  • Stefania Bellavia
  • Benedetta Morini
    • Categories Nonlinear Optimization Tags , , ,

    Trust-region methods for solving large bound-constrained nonlinear systems are considered. They allow for spherical or elliptical trust-regions where the search of an approximate solution is restricted to a low dimensional space. A general formulation for these methods is introduced and global and superlinear/quadratic convergence is shown under standard assumptions. Viable approaches for implementation in conjunction … Read more