Unconstrained Minimization

  • David G. Hull
Part of the Mechanical Engineering Series book series (MES)


This chapter is begun by discussing differentials and how they can be used to derive Taylor series expansions one term at a time. Parameter optimization begins by considering the minimization of a function of unconstrained (independent) variables. First, the conditions for minimizing a function of one variable are derived. It is shown that necessary conditions for a minimum are that the first differential of the performance index must vanish and that the second differential must be nonnegative. Given a point that satisfies the necessary conditions, the sufficient condition for a minimum is that the second differential be positive. A function of two independent variables is considered next, and then the generalization to n variables follows.


Saddle Point Taylor Series Performance Index Minimal Point Optimal Point 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • David G. Hull
    • 1
  1. 1.Aerospace Engineering and Engineering MechanicsThe University of Texas at AustinAustinUSA

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