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
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
Hopefully it will be ready before too long.
