Dual Simplex Method

Abstract

Consider the canonical problem

$$ f(x) = \left\langle {c,x} \right\rangle \to \inf ,x \in X = \left\{ {x \in {E^n}:x \ge 0,Ax = b} \right\} $$

((3.1.1))

where A is an m × n matrix, c ∈ E ⁿ, b ∈ E ^m. Let r = rank A = m. We shall give one more method for solving this problem which is customarily called a dual simplex method [1, 75]. In literature this method is also known as the method of successive refinement of estimates [98]. In what follows, we shall call the simplex method with anticyclin described in Chapter 1 the main simplex method.