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There was this course in many undergraduate mathematics programs called integer programming. It included Modelling, Linear Programming Primal, Linear Programming Duality, Dual Simplex Algorithm and Alternative IP Formulations, Total unimodularity, sub-modularity, Matroids, Branch and Bound, Delayed Column Generation, Branch and Price, Lagrangian Relaxation, Lagrangian Dual, Cutting Planes, Gomory Cuts, Branch and Cut. I am a high school student and know introductory university mathematics, such as single and multivariable calculus, ordinary differential equations and elementary linear algebra(I read linear algebra by Gilbert Strang).

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    $\begingroup$ You must be a master of linear algebra, as was the case in my linear and integer programming courses. Don't rush it, though. $\endgroup$ Commented Jul 10, 2022 at 23:30
  • $\begingroup$ You should make a point to include your Question statement in the body of the Question, not only in the title. The extra space allows you to put the request in a context that makes it clearer to Readers what kind of response will be helpful. $\endgroup$ Commented Jul 10, 2022 at 23:33
  • $\begingroup$ Hi: In the 1980's, nemhauser and wolsley was the bible for integer programming-combinatorics. I don't know if it still is but you should take a look at it and see whether it works for you. It's pretty advanced. P.S. Just my opinion but to get into integer programming at your age, might be rushing things. It's a pretty specific area. You might want to get the broader picture first, even if it was just through an operations research text. That would be more helpful as far as telling you whether you like the field. $\endgroup$ Commented Jul 11, 2022 at 0:01
  • $\begingroup$ Although it doesn’t cover integer programming, I recommend reading Convex Optimization by Boyd and Vandenberghe. Especially the first five chapters. $\endgroup$ Commented Jul 11, 2022 at 0:37
  • $\begingroup$ @Arham: The 1998 book recommended below is probably more useful than the 80's one I mentioned in the comment. I didn't know that he had a more updated and solo text. $\endgroup$ Commented Jul 11, 2022 at 3:57

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You might be interested in Wolsey’s Integer Programming (1998).

See also https://or.stackexchange.com/questions/8333/books-for-integer-and-mixed-integer-programming

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