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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Minima of Functions of Several Variables with Inequalities as Side Conditions
verfasst von : William Karush
Erschienen in: Traces and Emergence of Nonlinear Programming
Verlag: Springer Basel
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The problem of determining necessary conditions and sufficient conditions for a relative minimum of a function
$$ f({x_1},{x_2},....,{x_n})$$
in the class of points
$$ x = ({x_1},{x_2},....,{x_n})$$
Satisfying the equations
$$ \rm {g_{\alpha}(X)= 0 (\alpha = 1, 2,....,m),} $$
where the functions f and g
α
have continuous derivatives of at least the second order, has been satisfactorily treated [1]
*
. This paper proposes to take up the corresponding problem in the class of points x satisfying the inequalities
$$ \begin{array}{clcclclclcl}\rm {g_{\alpha}(x)\geqq 0} & & & & & & \rm{\alpha = 1,2,...,m}\end{array} $$
where m may be less than, equal to, or greater than n.