Traces and Emergence of Nonlinear Programming pp 217-245 | Cite as

# Minima of Functions of Several Variables with Inequalities as Side Conditions

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## Abstract

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.

## Keywords

Linear Inequality Relative Minimum Inductive Proof Admissible Curve Admissible Direction## Preview

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