Minima of Functions of Several Variables with Inequalities as Side Conditions

William Karush

A chapter in Traces and Emergence of Nonlinear Programming, 2014, pp 217-245 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0439-4_10

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DOI: 10.1007/978-3-0348-0439-4_10

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