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- Title
Optimal Control with Integral State Equations.
- Authors
Kamien, M. I.; Muller, E.
- Abstract
The article presents information on optimal control with integral state equations. The articles presents a theorem similar to V.L. Bakke's and V.R. Vinokurov's, which is suitable for dealing with such problems in a more straightforward, systematic fashion. A second theorem indicating circumstances under which the necessary conditions are also sufficient follows. The capital replacement problem is then solved and an extension of the M. Nerlove-K.J. Arrow result regarding the optimal ratio of advertising goodwill to sales is then presented. A simplified version of a theorem of Bakke for optimal control with an integral state equation has been presented. Usual concavity conditions have been shown to render the necessary conditions for an optimum sufficient as well. Finally, application of this Maximum Principle to some capital replacement problems has demonstrated how they might be treated in a uniform fashion.
- Subjects
CONTROL theory (Engineering); INTEGRAL equations; EQUATIONS; MATHEMATICAL models of investments; CAPITAL stock; FUNCTIONAL equations; DIFFERENTIAL equations; SALES; ADVERTISING; ECONOMETRIC models; BUSINESS; MATHEMATICAL models
- Publication
Review of Economic Studies, 1976, Vol 43, Issue 3, p469
- ISSN
0034-6527
- Publication type
Article
- DOI
10.2307/2297225