4. Simplex method

The simplex method was developed by G. Dantzig (1947). It comprises two phases:

phase 1 – initialization: find a feasible basic solution (or detect the impossibility: $D_{R} = ϕ$ );
phase 2 – progression: move from one vertex to a neighbouring vertex to increase the objective function F (or detect a non-major objective function F).

The terminology of the simplex method comes from the fact that we call n-simplex, or simply simplex, the convex envelope of a set of n + 1 points (n = 1: a segment, n = 2: a triangle, n = 3: a tetrahedron).

We'll start by describing phase 2, i.e....

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource.
Click here to request your free trial access!

Already subscribed? Log in!

The Ultimate Scientific and Technical Reference

A Comprehensive Knowledge Base, with over 1,200 authors and 100 scientific advisors

+ More than 10,000 articles and 1,000 how-to sheets, over 800 new or updated articles every year

From design to prototyping, right through to industrialization, the reference for securing the development of your industrial projects

This article is included in

Mathematics

This offer includes:

Knowledge Base

Updated and enriched with articles validated by our scientific committees

Services

A set of exclusive tools to complement the resources

Practical Path

Operational and didactic, to guarantee the acquisition of transversal skills

Doc & Quiz

Interactive articles with quizzes, for constructive reading

Subscribe now!

Ongoing reading
Simplex method

Previous
page Feasible basic solutions and their geometric properties

Implementing the simplex method

Bibliography

(1) - BILLIONNET (A.) - Optimisation discrète – De la modélisation à la résolution par des logiciels de programmation mathématique. - Dunod (2007).
(2) - BREZINSKI (C.) - Initiation à la programmation linéaire et à l'algorithme du simplexe. -...