Linear optimization is the problem of achieving the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships, and it is one of the most fundamental topics in computational optimization. The simplex method, the main algorithms used to solve linear optimization problems, is regarded as one of the most influential algorithms in science and engineering in the 20th century.
In this course we take a theoretical and algorithmic approach: we gain insight into the structure of the problem, and we develop both a geometric and an algebraic understanding of its properties. We investigate the theory of linear optimization in depth, and a number of results will be formally proven. The course requires a working knowledge of linear algebra, and a certain mathematical maturity. Students are expected to express their reasoning in a rigorous way, for example they will be asked to write proofs in assignments and on exams.