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.
KeywordsSaddle Point Taylor Series Performance Index Minimal Point Optimal Point
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