Adapting Broyden Method to Handle Linear Constraints Imposed via Lagrange Multipliers

Author (s): Rodríguez-Ferran, A. and Huerta, A.
Journal: International Journal for Numerical Methods in Engineering

Volume: 46, Issue 12
Pages: 2011 – 2026
Date: 1999


Various nonlinear equation solvers are adapted to handle linear constraints via
the Lagrange-multiplier technique. This adaptation process turns out to be quite
straightforward for Newton-Raphson methods and rank-two Quasi-Newton methods (BFGS
and DFP), but rather more involved for Broyden method. In fact, two Broyden methods
can be obtained: the standard one and a modified one, better adapted to the Lagrange-multiplier
environment. Some numerical examples are used to assess the relative performance
of the various adapted solvers.



  Author   = {A. Rodr\'{\i}guez-Ferran and A. Huerta},
  Title    = {Adapting {B}royden method to handle linear constraints imposed via {L}agrange multipliers},
  Fjournal = {International Journal for Numerical Methods in Engineering},
  Journal  = {Int. J. Numer. Methods Eng.},
  Volume   = {46},
  Number   = {12},
  Pages    = {2011--2026},
  Year     = {1999}}