A turnpike property in an eigenvalue optimization problem

TL;DR

This paper proves a turnpike property in a constrained eigenvalue optimization problem related to mRNA translation, revealing a specific structure in optimal parameters with implications for nonlinear dynamical models.

Contribution

It provides the first rigorous proof of a turnpike property in an eigenvalue optimization problem, connecting concepts from optimal control and biological modeling.

Findings

Optimal parameters exhibit a three-part structure with a middle segment of approximately equal values.

The first and third parts of the parameter list are relatively short.

This is the first known proof of a turnpike property in an eigenvalue optimization context.

Abstract

We consider a constrained eigenvalue optimization problem that arises in an important nonlinear dynamical model for mRNA translation in the cell. We prove that the ordered list of optimal parameters admits a turnpike property, namely, it includes three parts with the first and third part relatively short, and the values in the middle part are all approximately equal. Turnpike properties have attracted considerable attention in econometrics and optimal control theory, but to the best of our knowledge this is the first rigorous proof of such a structure in an eigenvalue optimization problem.