Title: Mixed-Integer Nonlinear Programs with On-Off Constraints
Abstract: We study optimization problems that have both nonlinear functional relationships between decision variables and 0-1 indicator variables that turn on and off these relationships. Problems of this class occur in many areas, including statistics, financial engineering, and engineering design. After reviewing earlier work on a reformulation technique applicable to the case when the nonlinear functions are separable, we discuss on-going research aimed at attacking the non-separable case. Our primary focus will be on the case when the nonlinearities are quadratic.