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Minima of Functions of Several Variables with Inequalities as Side Conditions

Chapter

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 gα 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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

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