Journal of Optimization Theory and Applications

, Volume 23, Issue 4, pp 563–579

Nearest feasible paths in optimal control problems: Theory, examples, and counterexamples

  • S. P. Sethi
Contributed Papers

DOI: 10.1007/BF00933297

Cite this article as:
Sethi, S.P. J Optim Theory Appl (1977) 23: 563. doi:10.1007/BF00933297

Abstract

Many infinite-horizon optimal control problems in management science and economics have optimal paths that approach some stationary level. Often, this path has the property of being the nearest feasible path to the stationary equilibrium. This paper obtains a simple multiplicative characterization for a single-state single-control problem to have this property. By using Green's theorem it is shown that the property is observed as long as the stationary level is sustainable by a feasible control. If not, the property is, in general, shown to be false. The paper concludes with an important theorem which states that even in the case of multiple equilibria, the optimal path is a nearest feasible path to one of them.

Key Words

Optimal controlGreen's theoreminfinite horizonmultiplicative problemsoptimal stationary equilibriumeconomic applications

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • S. P. Sethi
    • 1
  1. 1.Faculty of Management StudiesUniversity of TorontoTorontoCanada