Prerequisites

Abstract

Linear Programs are special mathematical programming problems. We understand by a mathematical programming problem in the Euclidean space ℝn the optimization of a given real-valued function — the objective function — on a given subset of ℝn, the so-called feasible set. A mathematical programming problem is called a linear program if its objective function is a linear functional on ℝn and if the feasible set can be described as the intersection of finitely many halfspaces and at most finitely many hyperplanes in ℝn. Hence the feasible set of a linear program may be represented as the solution set of a system of finitely many linear inequalities and, at most, finitely many linear equalities — the so-called (linear) constraints — in a finite number of variables.