The Role of Convexity in Discrete Optimization

Abstract

Though the notions of convex sets and discrete programming seem in an first instance quite unrelated, convexity plays a remarkable role in discrete programming. Discrete optimization problems ask for maximizing or minimizing functions in real variables where some or all of the variables are supposed to take only integer values. We distinguish two main problems: mixed-integer programming problems where some variables are restricted to integral values and combinatorial optimization problems with zero-one variables.