Numerical experience with iterative methods for equality constrained nonlinear programming problems

Abstract

We show that indefinitely preconditioned symmetric Krylov-subspace methods are very efficient for solving linearized KKT systems arising in equality constrained optimization. We give a numerical comparison of various Krylov subspace methods in three different forms (original system, null-space transformation, range-space transformation). Furthermore, we give a survey of our previous results concerning indefinite preconditioners and merit functions and prove new propositions.

Keywords:

• Nonlinear programming
• Sparse problems
• Equality constraints
• Inexact Newton method
• Line search methods
• Indefinite systems
• Indefinite preconditioners
• Symmetric Krylov subspace methods
• Residual smoothing
• Computational experiments