# The interval turnpike property for adjoints

arXiv: https://arxiv.org/abs/2005.12120 · HTML: https://mlsanity.com/paper/2005.12120/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2020.

## Built on by (most cited first, 1 of 1)

- [Tuning the burn-in phase in training recurrent neural networks improves their performance](https://mlsanity.com/paper/2602.10911/) (2026)

## Abstract (arXiv)

In this work we derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further give stronger estimates for analytic semigroups and provide a numerical example with a boundary controlled semilinear heat equation to illustrate the results.