Easy Linear Optimization

Linear Optimization deals with certain simple kinds of optimization problems, namely, the ones which can be formulated as finding the optimum of a linear function on a set constrained by linear inequalities. Such programs arise naturally in economics and computer science.

The area of linear optimization is well-studied since the works of L. Kantorovich and G. Dantzig. Most undergraduate books in this area fix the field of reals or rationals right from the start. While convenient, there is no need for such a restriction of the field. It is well-known that working over any subfield of the reals does not hurt: the overwhelming majority of the theory and algorithms require no substantial change of the high-level view; one has to pay attention only to the low-level proofs. Our treatise takes such an approach: it develops the theory of linear programming over an arbitrary subfield of the real numbers right from the start. This approach is an advantage for an undergraduate student, who typically knows what a field and a subfield are from his/her initial lectures on linear algebra.