Developing the Simplex Method with NumPy and Matrix Operations
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In this post, I seek to address the paucity of resources describing and implementing the Simplex Method from a matrix operations perspective. In particular, most computational implementations of the Simplex Method are developed by directly implementing the Simplex tableau method.
As such, in this post I seek to give an alternative implementation of the Simplex Method by developing a program of the Simplex Method that leverages matrix operations instead of the tableau method. I avoid the mathematics of the particular matrix operations implementation to keep this post concise, however if the reader wishes to learn more about the mathematics of this particular implementation, they can refer to the book Linear and Nonlinear Programming by Stephen Nash and Ariela Sofer, which gives a great introduction into the Simplex Method and the many ways to implement it. The book Linear Programming and Network Flows by Bazaraa, Jarvis, and Sherali is also a great in-depth resource that touches upon many of the ideas mentioned in this post.
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