Research Reports from the Department of Operations

Document Type

Report

Publication Date

1-1-1967

Abstract

The mathematical programming problem -- find a non-negative n-vector x which maximizes f(x) subject to the constraints g^i(x) ≥ 0, i = 1,...,m -- is investigated where f(x) is assumed to be concave or strictly quasi-concave and the g^i(x) are monotonic increasing functions. It is shown that under certain conditions on g^i(x), the Kuhn-Tucker-Lagrange conditions are necessary and sufficient for the optimality of x*. It is also shown that the g^i(x) are an interesting class of functions since, among other properties, they are closed under non-negative addition, under the addition of any scalar, and under multiplication of non-negative members of the class.

Keywords

Operations research, Mathematical optimization, Programming (Mathematics), Constrained optimization, Lagrangian functions, Nonlinear programming, Mathematical analysis

Publication Title

Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University

Issue

Technical memorandum no. 74

Rights

This work is in the public domain and may be freely downloaded for personal or academic use

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