A systematic and rapid steepest-ascent numerical procedure is described for solving two-point boundary-value problems in the calculus of variations for systems governed by a set of nonlinear ordinary differential equations. Numerical examples are presented for minimum time-to-climb and maximum altitude paths for a supersonic interceptor and maximum-range paths for an orbital glider.
A Steepest-Ascent Method for Solving Optimum Programming Problems
A. E. Bryson,
A. E. Bryson
Division of Engineering and Applied Physics, Harvard University, Cambridge, Mass.
W. F. Denham
Missiles & Space Division, Raytheon Company, Bedford, Mass.
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Bryson, A. E., and Denham, W. F. (June 1, 1962). "A Steepest-Ascent Method for Solving Optimum Programming Problems." ASME. J. Appl. Mech. June 1962; 29(2): 247–257. https://doi.org/10.1115/1.3640537
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