Abstract
It is proven here that a bounded perturbation of the discrete dynamic programming functional equation arising from the Bolza problem yields a bounded change in its solution. This stability property encourages the development of approximation techniques for solving such equations. One such technique, involving the backward solution of an approximate functional equation as a prediction step, followed by a forward reconstruction using true equations as a correction step, is then discussed. Bounds for the errors arising from such an approximation procedure are derived. Successive approximations is suggested, in conclusion, as a means for obtaining improved solutions.
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References
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Communicated by R. E. Kalaba
This research was supported in part by the National Science Foundation under Grant No. GP-29049, in part by the Atomic Energy Commission, Division of Research, under Contract No. AT(40-3)-113, Project 19, and in part by the US Army Research Office, under Grant No. DAHC04-74-G-0110.
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Lew, A. Stability, prediction-correction, and dynamic programming. J Optim Theory Appl 17, 239–250 (1975). https://doi.org/10.1007/BF00933878
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DOI: https://doi.org/10.1007/BF00933878