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Augmented Penalty Function Technique for Optimal Control Problems

  • M. Vlach
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 157)

Abstract

Let f,g1,g1 g2,…gm be real functions of n variables x1,…xn. ConsIDer the problem
$$\matrix{ {\min imize} \hfill & {f(x)} \hfill \cr {subject\,to} \hfill & {g_i (x) = Q, i = 1,2, \ldots, m.} \hfill \cr } $$
(1)
Penalty function methods obtain a solution to the preceding problem as a limit of solutions of suitable chosen unconstrained problems.

Keywords

Optimal Control Problem Gradient Method Penalty Function Mathematical Programming Problem Unconstrained Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Reference

  1. [1]
    Eestenes, M.R., “Multiplier and Gradient Methods,” Journal of optimization Theory and Applications, Vol 4 (1969), pp. 303–320.CrossRefGoogle Scholar
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    Arrow, K.J. and R.M.. Solow, “Gradient Methods for Constrained Maxima with Weakened Assumptions” In K.J. Arrow,L. Hurwicz; and H. Uzawa,.. Studies in Linear and Monlinear Programming, Stanford University Press, Stanford, California, 1958.Google Scholar
  3. [3]
    Miele, A., JU, Cragg, E.E. Iyer, R.R and A.V. Levy, “Use of the Augmented Penalty Function in Mathematical Programming Problems”, Journal of Cptimization. Theory and Applications, Vol 8 (1971), pp. 115–153.CrossRefGoogle Scholar
  4. [4]
    Connor M.A. and M. Vlach “A New Augmented Penalty Function technique for Optimal Control Problems”, Journal of Optimization Theory and Applications, Vol 21 (1977) pp 33–49.Google Scholar
  5. [5]
    O’Doherty, R.J. and B.L. Piercon, “A numerical Study of Augmented Penalty Function Algorithm for Terminally Constrained Optimal Control Problems”, Journal of Optimization Theory and Applications, Vol 14 (1974), pp. 393–403.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin HeIDelberg 1978

Authors and Affiliations

  • M. Vlach
    • 1
  1. 1.Department of Cybernetics and Operations ResearchCharles UniversityPragueCzechoslovakia

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