Approximate Nullspace Iterations for KKT Systems

The aim of the paper is to provide a theoretical basis for approximate reduced SQP methods. In contrast to inexact reduced SQP methods, the forward and the adjoint problem accuracies are not increased when zooming in to the solution of an optimization problem. Only linear-quadratic problems are treated, where approximate reduced SQP methods can be viewed as null-space iterations for KKT systems. Theoretical convergence results are given. Numerical examples illustrate the results and show that convergence also holds in cases when the assumptions guaranteeing convergence are not satisfied. Key words. KKT systems, appoximate reduced SQP methods, iterative solvers. AMS subject classifications. 65F10,65K05,90C20, 93C20.

• Type: Journal
• Year: 2010
• Where: SIAMMAX
• Authors: Kazufumi Ito, Karl Kunisch, Volker Schulz, Ilia Gherman
• Keywords: Approximate Reduced Sqp, KKT Systems, SIAMMAX 2010, SQP Methods