A turnpike property in an eigenvalue optimization problem

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.