Research Reports from the Department of Operations
Document Type
Report
Publication Date
12-1-1967
Abstract
The mathematical programming problem--find a non-negative n-vector x which maximizes f(x) subject to the constraints gᵢ(x) ≥ 0, i = 1,...,m — is investigated where f(x) is assumed to be concave or pseudo-concave and the gᵢ(x) are increasing functions. It is shown that under certain conditions on gᵢ(x), the Kuhn-Tucker-Lagrange conditions are necessary and sufficient for the optimality of x*. It is also shown that the gᵢ(x) are a useful 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. Examples of the above programming problem with increasing constraint functions are found in many chance-constrained programming problems.
Keywords
Operations research, Mathematical optimization, Nonlinear programming, Lagrangian functions, Concave functions, Constraint programming (Computer science)
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 101
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Pierskalla, William P., "Mathematical Programming with Increasing Constraint Functions" (1967). Research Reports from the Department of Operations. 287.
https://commons.case.edu/wsom-ops-reports/287