Penalty function techniques: A tutorial

This tutorial surveys several unconstrained methods for solving constrained mathematical programming problems. The paper presents a historical development of the transformation approach in order to give a general sense for the appropriateness of these methodologies. The ideas presented here serve as a general introduction to those who wish to acquaint themselves to this area without assuming that the reader is a mathematician or a mathematical programmer. Strengths, weaknesses, and improvements to various procedures are subsequently presented in order to encourage the use of the methods to solve real-world problems that frequently present themselves to industrial engineers.