# Perturbation of Linear Programs

Consider the linear program,

$$\begin{array}{ll} \text{maximize} & c^T x\\ \text{subject to} & Ax \leq b\\ & x \geq 0\end{array}$$

I want to study the sensitivity of the optimal $x^*$ with small perturbations to the matrix $A$. Most of the results I can find consider sensitivity with respect to $b$. Can some one point me to the relevant literature?

## 2 Answers

Perhaps Harvey Greenberg has written about that. I.e. http://math.ucdenver.edu/~hgreenbe/booksEtc/GreenbergCh3.pdf

• Thanks for the reference. I will read this and get back. Apr 11 '16 at 15:46

A recent paper, Journal of the Operational Research Society (2016),67,450-456, Emeritus Professor H. Paul Williams produced some interesting and best possible results on the Fourier-Motzkin method which might possibly be of research interest to you . The paper was titled " The Dependency Diagram of a Linear Programme" .