Formulation of integer programming problems and the characterization of optimization problems representable as integer and mixed-integer programs. The degree of difficulty of classes of integer programs and its relation to the structure of their feasible sets. Optimality conditions. Branch-and-bound, cutting plane, and decomposition methods for obtaining solutions or approximating solutions. Prereq: CS 525 or consent of instructor. Note: This course is no longer offered regularly; those interested in the topic should take CS 728, Integer Optimization, instead.