This account of turnpike theorems concentrates on the discrete time model, descended from the early von Neumann growth model and the Dosso model. It portrays the current state of the theory under the following five headings: (i) a turnpike in the von Neumann model, (ii) a turnpike in the Ramsey...

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function consisting of a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known. Further, we consider both cases: unconstrained and...

We present a substantive and far-reaching generalization of the principal results in the economics of forestry, as formalized by Mitra and Wan (1986). Rather than a polarized dichotomy of linear and strictly concave, differentiable benefit (felicity) functions, we develop the theory in the...

This 2012 perspective of the 1987 Palgrave entry on ‘turnpike theory’ highlights the subsequent development of the subject in the light of a critical re-reading of the original. It distinguishes the 1949 conception, a response of Samuelson to a 1945 von Neumann challenge to the...

Linking the statistic and the machine learning literature, we provide new general results on the convergence of stochastic approximation schemes and inexact Newton methods. Building on these results, we put forward a new optimization scheme that we call generalized inexact Newton method (GINM)....

Linking the statistic and the machine learning literature, we provide new general results on the convergence of stochastic approximation schemes and inexact Newton methods. Building on these results, we put forward a new optimization scheme that we call generalized inexact Newton method (GINM)....