ABSTRACT
This chapter presents an introduction to the mathematical programming problem. It introduces both the linear programming problem and the nonlinear programming problem. The chapter discusses the nature of the solutions of these problems. The concepts of local and global solutions are analogous to those found in calculus. The chapter describes post optimal analysis, parametric programming, and stability of solutions. It provides a brief historical outline of the major optimization techniques. The chapter deals primarily with optimization problems which possess continuous variables. The process of using an optimal solution for an existing problem to obtain an optimal solution for a modified problem is called post-optimal analysis. One of the first mathematical programming problems to be formulated was the transportation problem. A related problem, known as the dual linear programming problem, was formulated by John Von Neuman. Von Neuman along with others like A. W. Tucker and A. C. Williams were instrumental in the development of a basic duality theory.
