The Concept of Degeneracy

Abstract

Consider the system of linear inequalities

$$Ax\le b,x\ge 0,{{(A\in I{{R}^{mxn}},b\in I{{R}^{m}})}^{1)}}$$

(2.1)

$$b\ge 0.$$

(2.2)

The condition (2.2) ensures that the solution set²⁾

$$X=\{x\in I{{R}^{n}}|Ax\le b,x\ge 0\}$$

(2.3)

is nonempty and thus always a polyhedral set³⁾ having at least one vertex. Denote by X the solution set of the canonical form of (2.1)⁴⁾. Each basis B of the enlarged matrix P =(AüI) is also called a basis of (2.1) or of the canonical form. Tab. 2.1 shows the pivot tableau which is uniquely assigned to a basis B (and vice versa)⁵⁾.