Reduced Simplex Method

Ping-Qi Pan
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Ping-Qi Pan: Southeast University, Department of Mathematics

Chapter Chapter 15 in Linear Programming Computation, 2014, pp 357-385 from Springer

Abstract: Abstract In this chapter and the following two chapters, some special forms of the LP problem, introduced in Sect. 25.1, will be employed to design new LP methods. In particular, this chapter will handle the so-called “reduced problem” (25.2), i.e., 15.1 min x n + 1 , s . t . ( A ⋮ a n + 1 ) x x n + 1 = b , x ≥ 0 , $$\displaystyle{ \begin{array}{l@{\;\;}l} \min \;\;&x_{n+1}, \\ \mathrm{s.t.}\;\;&(A\ \vdots\ a_{n+1})\left (\begin{array}{c} x\\ x_{n+1} \end{array} \right ) = b,\quad x \geq 0,\\ \;\;\end{array} }$$ where a n + 1 = − e m + 1 $$a_{n+1} = -e_{m+1}$$ . Note that the objective variable x n+1 is in the place of f (thereafter the two will be regarded equal), and hence there is no sign restriction on x n+1.

Keywords: Dual Feasibility; Conventional Simplex; Simplex Tableau; Basic Optimal Solution; Auxiliary Tableau (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-642-40754-3_15

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