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A new solution property in optimal control: The lens |
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| Authors: | Gustav Feichtinger Peter M Kort Yuri A Yegorov |
| Affiliation: | a Department of Operations Research and Nonlinear Dynamical Systems, Vienna University of Technology, Vienna, Austria b Department of Business Studies, University of Vienna, Vienna, Austria c Department of Econometrics and Operations Research & CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands d Department of Economics, University of Antwerp, Antwerp, Belgium e Institute for Advanced Studies, Vienna, Austria |
| Abstract: | We consider a new property of an optimal control problem called a lens.A lens is an interior point in the state-control phase plane where—given the value of the state variable—there is only one control value satisfying the necessary optimality conditions and—given the value of the control variable—there is only one state value satisfying the necessary optimality conditions.We build a simple model that generates a lens and give necessary and sufficient conditions under which a lens occurs. |
| Keywords: | Optimal control Maximum principle Phase plane Economic dynamics |
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