Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints

Abstract

We propose a nonlinear additive Schwarz method for solving nonlinear optimization problems with bound constraints. Our method is used as a "right-preconditioner" for solving the first-order optimality system arising within the sequential quadratic programming (SQP) framework using Newton's method. The algorithmic scalability of this preconditioner is enhanced by incorporating a solution-dependent coarse space, which takes into account the restricted constraints from the fine level. By means of numerical examples, we demonstrate that the proposed preconditioned Newton methods outperform standard active-set methods considered in the literature