Introduction

Abstract

When attempting to optimize the performance or design of a system, it is often pos-sible to formulate the underlying problem as the minimization or maximization of a specific objective function subject to a variety of physical, technical, and operational constraints. Typical examples include the minimization of transportation costs sub-ject to capacity restrictions on delivery vehicles and time restrictions on customer visits, the minimization of the sum of the absolute errors between a given data set and an approximating function, and the maximization of expected returns from an investment portfolio subject to acceptable risks levels and cash flow requirements. In each of these instances, mathematical programming provides a general framework for modeling the problem and organizing the data. With the growth of theory and the expansion of applications it is natural to partition the field according to the types of functions used in the models and the nature of the decision variables — discrete, continuous, or parametric. The discipline known as nonlinear programming plays a fundamental role in almost all areas of optimization and has proven its worth in the design, planning, and control of many different types of systems.