The Simplex Method

David G. Luenberger and Yinyu Ye
Additional contact information
David G. Luenberger: Stanford University
Yinyu Ye: Stanford University

Chapter Chapter 4 in Linear and Nonlinear Programming, 2021, pp 77-127 from Springer

Abstract: Abstract The idea of the simplex method is to proceed from one basic feasible solution (that is, one extreme point) of the constraint set of a problem in standard form to another, in such a way as to continually improve the value of the objective function until an optimum is reached. The results of Chap. 2 assure us that it is sufficient to consider only basic feasible solutions in our search for an optimal feasible solution. The results of Chap. 3 establish a termination criterion and provide a dual certificate for a basic feasible solution to be optimal. This chapter demonstrates that an efficient method for moving among basic feasible solutions to the optimum can be constructed. Moreover, we obtain both optimal primal and optimal dual solutions upon the termination, or show that either the primal or the dual is infeasible.

Date: 2021
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-3-030-85450-8_4

Ordering information: This item can be ordered from
http://www.springer.com/9783030854508

DOI: 10.1007/978-3-030-85450-8_4

Access Statistics for this chapter

More chapters in International Series in Operations Research & Management Science from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().