PhD-level textbooks on linear programming

My graduate Linear Programming class uses Bertsimas & Tsitsiklis's Introduction to Linear Optimization. Are there any alternative texts that I could use to supplement this textbook (mainly the content of Chapter 2 of Bertsimas & Tsitsiklis: extreme point, vertex, basic feasible solution, contains/does not a line, Fourier-Motzkin) at the same level rigor and which contain exercises that I could practice on?

Ideally, I would also like a book with a decent (the more the better) number of pictures that gives geometric intuition behind proofs.

A classic textbook that does a really good job of building from the fundamentals is Theory of Linear and Integer Programming by Schrijver. Chapter 7 in particular gives great intuition on linear programming.

These lecture notes by Ryan O'Donnell and Anupam Gupta are also a good, quicker reference as well as the textbook they refer to, Understanding and Using Linear Programming by Matoušek and Gärtner.

• thanks @ydubey7. i think perhaps schrijver is a bit more high level than bertsimas. I really like gartner although i don't believe there's any exercises. are there any books similar to bertsimas chapter 2 with exercises I can practice on. Oct 5 '19 at 23:25

I used to study with the following book:

Chvatal, V. (1983). Linear programming.

Overall it's very clear. It's written primary for graduate courses in operations research, math and computer science. Chapter 17: Connections with Geometry, may give some geometric intuitions.

I hope it helps you.

There are some good problems in Linear Optimization: Theory and Extensions by Fang and Puthenputra. Chapter 2 of the book ("Geometry of Linear Programming") is most comparable to Chapter 2 of Bertsimas.

Also see this related question on Math.SE: https://math.stackexchange.com/q/20643/669798

• thanks, ill check it out. Oct 5 '19 at 2:10

G.B. Dantzig and M.N. Thapa Linear Programming 1: Introduction, Springer, 1997 and Linear Programming 2: Theory and Extensions, Spinger, 2003.

Linear Programming 2, Theory and Extensions, is the one with the hard-core theoretical Linear Programming Ph.D. material which you seem to want. Among other things, it contains some of the old Stanford O.R. Ph.D. comprehensive exam questions in Linear Programming - you won't find that in any other book.