ABSTRACT
This chapter describes an algebraic step-by-step procedure, called the simplex algorithm that can be applied to solve linear programming problems with any number of decisions and constraints. An optimization problem is characterized by its specific objective function that is to be maximized or minimized, depending upon the problem and, in the case of a constrained problem, a given set of constraints. Possible constraints include those that represent limited budgets or resources, non-negativity constraints on variables and conservation equations. Complementarity is a new domain of applied mathematics, having deep relations with several aspects of fundamental mathematics and numerical analysis. Complementarity problems represent a wide class of mathematical models related to optimization, economics, engineering, mechanics, elasticity, fluid mechanics and game theory. Variational inequality theory was introduced by Hartman and Stampacchia as a tool for the study of partial differential equations with applications arising from mechanics. It describes such variational inequalities were infinite-dimensional rather than finite-dimensional.
