ABSTRACT
Nonlinear programming is the study of problems where a nonlinear function has to be minimized or maximized over a set of values in Rn delimited by several nonlinear equalities and inequalities. Such problems are extremely frequent in engineering, science, and economics. Since World War II, mathematicians have been engaged to solve problems of resource allocation, optimal design, and industrial planning involving nonlinear objective functions as well as nonlinear constraints. These problems required the development of new algorithms that have been benefited with the invention of digital computers. This chapter is concentrated on presenting the fundamentals of deterministic algorithms for nonlinear programming. Our purpose is to present a summary of the basic algorithms of nonlinear programming. A pseudocode for each algorithm is also presented. We believe that our presentation in terms of a fast cookbook for nonlinear programming algorithms can benefit the practitioners of operations research and management science.
