# Turnpike Properties in Discrete-Time Mixed-Integer Optimal Control

arXiv: https://arxiv.org/abs/2002.02049 · HTML: https://mlsanity.com/paper/2002.02049/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2020.

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

- [On the Turnpike to Design of Deep Neural Nets: Explicit Depth Bounds](https://mlsanity.com/paper/2101.03000/) (2021)

## Abstract (arXiv)

This note discusses properties of parametric discrete-time Mixed-Integer Optimal Control Problems (MIOCPs) as they often arise in mixed-integer NMPC. We argue that in want for a handle on similarity properties of parametric MIOCPs the classical turnpike notion from optimal control is helpful. We provide sufficient turnpike conditions based on a dissipativity notion of MIOCPs, and we show that the turnpike property allows specific and accurate guesses for the integer-valued controls. Moreover, we show how the turnpike property can be used to derive efficient node-weighted branch-and-bound schemes tailored to parametric MIOCPs. We draw upon numerical examples to illustrate our findings.