Introduction

Abstract

A crucial step in making decisions of a quantitative nature requires the solution of optimization problems. Such optimization problems can be described as minimizing or maximizing an objective function subject to a family of constraints. The choice of which functions to use as an objective function and as constraints depends on the modeling of the problem. However, modeling a problem is only useful in practice if there exist methods to solve the proposed model. This justifies the enormous popularity of linear programs, i. e. optimization problems where the objective function and the constraints are linear functions. In fact, a practical method, the popular simplex method, exists since the late forties to solve these problems. In spite of this, there are many real life situations which cannot be appropriately modeled using only linear functions and therefore the field of nonlinear programming has received increasing attention from many researchers.