On the complexity of nonlinear mixed-integer optimization

Abstract

This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained fully polynomial time approximation schemes in fixed dimension, and to strongly polynomial-time algorithms for special cases.

26 pages, 5 figures; to appear in: Mixed-Integer Nonlinear Optimization, IMA Volumes, Springer-Verlag