Approximate Nullspace Iterations for KKT Systems

Abstract

We investigate a linear iteration scheme for solving Karush–Kuhn–Tucker systems arising from optimization problems with linear equality constraints. The iterations are motivated by the simplicity of the proposed combination of iterations for the forward and adjoint systems that need to be solved and for which efficient solvers may already be available. Convergence results are derived, and their practical relevance is investigated by means of a numerical example.