# Preconditioning of Active-Set Newton Methods for PDE-constrained Optimal Control Problems

arXiv: https://arxiv.org/abs/1407.1144 · HTML: https://mlsanity.com/paper/1407.1144/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2014.

## Built on by (most cited first, 2 of 2)

- [Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems](https://mlsanity.com/paper/2307.00296/) (2023)
- [Learning to Control: The iUzawa-Net for Nonsmooth Optimal Control of Linear PDEs](https://mlsanity.com/paper/2602.12273/) (2026)

## Abstract (arXiv)

We address the problem of preconditioning a sequence of saddle point linear systems arising in the solution of PDE-constrained optimal control problems via active-set Newton methods, with control and (regularized) state constraints. We present two new preconditioners based on a full block matrix factorization of the Schur complement of the Jacobian matrices, where the active-set blocks are merged into the constraint blocks. We discuss the robustness of the new preconditioners with respect to the parameters of the continuous and discrete problems. Numerical experiments on 3D problems are presented, including comparisons with existing approaches based on preconditioned conjugate gradients in a nonstandard inner product.