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Journal of Optimization Theory and Applications

, Volume 183, Issue 2, pp 763–769 | Cite as

Extension of the Optimality Conditions for Unconstrained Parameter Optimization Problems Where the Standard Conditions Fail

  • David G. HullEmail author
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Abstract

The standard optimality conditions for an unconstrained minimal point in parameter optimization have been derived using admissible comparison points that lie on straight lines through the minimal point. While these conditions hold for most problems, there are problems where the second- and higher-order conditions give incorrect results. For these problems, some admissible comparison points must lie on curves through the minimal point. Then, the equations of the curves must be considered as constraints in the formation of the Taylor series. Two examples are presented: a problem with a curve minimum and the historical problem due to Peano.

Keywords

Parameter optimization Optimality conditions Curve minimum Peano’s problem 

Notes

References

  1. 1.
    Hancock, H.: Theory of Maxima and Minima. Dover Publications, New York (1960). (formerly published by Ginn and Company, 1917)zbMATHGoogle Scholar
  2. 2.
    Hull, D.G.: Optimal Control Theory for Applications. Springer, New York (2003)CrossRefzbMATHGoogle Scholar
  3. 3.
    Hull, D.G.: On the definition of a minimum in parameter optimization. J. Optim. Theory Appl. 175(1), 278–282 (2017)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of Texas at AustinAustinUSA

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