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


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.


Parameter optimization Optimality conditions Curve minimum Peano’s problem 



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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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