Bifurcations of Optimal Vector Fields

• 成果类型: Article
• 署名作者: Kiseleva, Tatiana; Wagener, Florian
• 署名单位: Vrije Universiteit Amsterdam; University of Amsterdam
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0655
• 发表日期: 2015
• 页码: 24-55
• 关键词: CONCAVE PRODUCTION FUNCTION; catastrophe-theory; optimal-growth; skiba points; MODEL; computation; thresholds; systems; paths

摘要

We study the structure of the solution set of a class of infinite-horizon dynamic programming problems with one-dimensional state spaces, as well as their bifurcations, as problem parameters are varied. The solutions are represented as the integral curves of a multivalued optimal vector field on state space. Generically, there are three types of integral curves: stable points, open intervals that are forward asymptotic to a stable point and backward asymptotic to an unstable point, and half-open intervals that are forward asymptotic to a stable point and backward asymptotic to an indifference point; the latter are initial states to multiple optimal trajectories. We characterize all bifurcations that occur generically in one-and two-parameter families. Most of these are related to global dynamical bifurcations of the state-costate system of the problem.