Five Preliminaries

Abstract

For every basic feasible solution x ∉ χ we have by Lemma 1 a feasible basis B. for every feasible basis B with index set I we have the reduced system

$$ x_B + B^{ - 1} Rx_R = \bar b $$

(4.1)

where $\bar b = B^{ - 1} b$. Hence a basic feasible solution x ∈ χ is defined by

$$ x_\ell = \bar b_{p\ell } for all \ell \in I, x_\ell = 0for all \ell \in N - I, $$

where pℓ is the position number of the variable ℓ ∈ I. if $I = \left\{ {k_1 , \ldots k_m } \right\}$, we can write equivalently

$$ x_{k_i } = \bar b_i for all 1 \leqslant i \leqslant m, x_\ell = 0for all \ell \in N - I. $$