Golden optimal path in discrete-time dynamic optimization processes. (English) Zbl 1179.90253

Elaydi, Saber (ed.) et al., Advances in discrete dynamical systems. Proceedings of the 11th international conference on difference equations and applications (ICDEA 06), Kyoto, Japan, July 24–28, 2006. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-49-5/hbk). Advanced Studies in Pure Mathematics 53, 77-86 (2009).
Summary: We are concerned with dynamic optimization processes from a viewpoint of Golden optimality. A path is called Golden if any state moves to the next state repeating the same Golden section in each transition. A policy is called Golden if it, together with a relevant dynamics, yields a Golden path. The problem is whether an optimal path/policy is Golden or not.
This paper minimizes a quadratic criterion and maximizes a square-root criterion over an infinite horizon. We show that a Golden path is optimal in both optimizations. The Golden optimal path is obtained by solving a corresponding Bellman equation for dynamic programming. This in turn admits a Golden optimal policy.
For the entire collection see [Zbl 1170.39300].


90C20 Quadratic programming
39A12 Discrete version of topics in analysis
49L20 Dynamic programming in optimal control and differential games