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G. Hurlbert Linear Optimization
Linear Optimization

Linear Optimization (formerly known as Linear Programming) essentially deals with optimizing linear functions over linear constraints. Of course, the subject is far richer than just that, reaching into convex geometry, linear algebra, probability, combinatorics, game theory, graph theory, and algorithms among other areas. It is also a springboard to related fields including integer, convex, and combinatorial optimization. I have recently published my undergraduate Linear Optimization textbook with Springer. In the process of writing I made a few discoveries that I am currently writing up: one regarding the equivalence of seemingly different implementations of the Simplex method, two involving combinatorial geometry, and another in graph theory. Also, I have invented a new algorithm for solving linear optimization problems (LOPs) that seems to behave nicely and run quickly. Some colleagues and I are writing code now for the community to test against existing algorithms on the standard testcases. Hopefully it will be ready before too long.