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Sequential conjugate-gradient-restoration algorithm for optimal control problems. Part 2. Examples

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Abstract

In Ref. 1, Heideman and Levy developed the sequential conjugate-gradient-restoration algorithm for minimizing a functional subject to differential constraints and terminal constraints. In this report, several numerical examples are presented, some pertaining to a quadratic functional subject to linear constraints and some pertaining to a nonquadratic functional subject to nonlinear constraints. These examples demonstrate the feasibility as well as the rapid convergence characteristic of the sequential conjugate-gradient-restoration algorithm.

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References

  1. Heideman, J. C., andLevy, A. V.,Sequential Conjugate-Gradient-Restoration Algorithm for Optimal Control Problems, Part 1, Theory, Journal of Optimization Theory and Applications, Vol. 15, No. 2, 1975.

  2. Ralston, A.,Numerical Integration Methods for the Solution of Ordinary Differential Equations, Mathematical Methods for Digital Computers, Vol. 1, Edited by A. Ralston and H. S. Wilf, John Wiley and Sons, New York, New York, 1960.

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  6. Miele, A., Pritchard, R. E., andDamoulakis, J. N.,Sequential Gradient-Restoration Algorithm for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 5, No. 4, 1970.

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Author notes

  1. J. C. Heideman (Engineering Specialist)

    Present address: Exxon Production Research Company, Houston, Texas

  2. A. V. Levy (Postdoctoral Fellow in Aero-Astronautics, Research Associate)

    Present address: CIMAS, Universidad Nacional Autonoma de Mexico, Mexico City, Mexico

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering and Materials Science, Rice University, Houston, Texas

    A. V. Levy (Postdoctoral Fellow in Aero-Astronautics, Research Associate)

Authors
  1. J. C. Heideman
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  2. A. V. Levy
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Additional information

This research was supported by the Office of Scientific Research, Office of Aerospace Research, United States Air Force, Grant No. AF-AFOSR-72-2185. The authors are indebted to Professor A. Miele for stimulating discussions and to Mr. J. M. Nocedal for verifying the numerical results.

Formerly, Graduate Student in Aero-Astronautics, Department of Mechanical and Aerospace Engineering and Materials Science, Rice University, Houston, Texas.

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Heideman, J.C., Levy, A.V. Sequential conjugate-gradient-restoration algorithm for optimal control problems. Part 2. Examples. J Optim Theory Appl 15, 223–244 (1975). https://doi.org/10.1007/BF02665294

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