Nearest Feasible Paths in Optimal Control Problems: Theory, Examples, and Counterexamples

Journal of Optimization Theory and Applications, Vol. 23, No. 4, pp. 563-579, December 1977

17 Pages Posted: 24 Jan 2008 Last revised: 1 May 2014

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: 1977

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.

Keywords: DNSS points, Nearest feasible paths, most rapid approach paths, MRAP, Optimal control, Green's theorem, infinite horizon, multiplicative problems, optimal stationary equilibrium, economic applications, Skiba points

JEL Classification: C61, C62, A19

Suggested Citation

Sethi, Suresh, Nearest Feasible Paths in Optimal Control Problems: Theory, Examples, and Counterexamples (1977). Journal of Optimization Theory and Applications, Vol. 23, No. 4, pp. 563-579, December 1977, Available at SSRN: https://ssrn.com/abstract=1086844

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
61
Abstract Views
965
Rank
637,858
PlumX Metrics