Structure of extremals of autonomous convex variational problems |
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| Institution: | 1. Psychology Department, Wayne State University, 71 West Warren Street, Detroit, MI 48202, USA;2. Department of Organizational Behavior, School of Industrial and Labor Relations, Cornell University, Ithaca, NY 14853, USA;3. The Pentagon, 300 Army, Washington, DC 203010-0300, USA;4. Psychology Department, University of Maryland, College Park, MD 20742, USA;1. Electrical and Computer Engineering, University of Minnesota, 200 Union Street, Minneapolis, MN 55455, USA;2. UCLA Mathematics Department, Los Angeles, CA 90095, USA;1. Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan;2. National Institute of Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan;3. National Institute of Advanced Industrial Science and Technology, 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, Japan |
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| Abstract: | In this paper we study the structure of approximate solutions of autonomous variational problems with convex integrands. We are interested in a turnpike property of the extremals which is independent of the length of the interval, for all sufficiently large intervals. To have this property means, roughly speaking, that the approximate solutions of the variational problems are determined mainly by the integrand, and are essentially independent of the choice of interval and endpoint conditions. |
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