Algorithms and computer-based tools for analyzing infeasible linear and nonlinear programs have been developed in recent years, but few such tools exist for infeasible mixed-integer or integer linear programs. One approach that has proven especially useful for infeasible linear programs is the isolation of an Irreducible Infeasible Set of constraints (IIS), a subset of the constraints defining ...

3 Main Results 8 3.1 Mixed-Integer Linear Programming Framework . . . . . . . . . . . . . . . . . . . . . 9 3.2 Initialization of Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Implementing Dynamical Equivalence and Linear Conjugacy . . . . . . . . . . . . . 10 3.4 Implementing Deficiency Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.5 ...

A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures ...

for installing a large number of sizes and types of items (e.g., machines) over time so as to optimize some measure (e.g., initial capital investment), subject to various resource constraints. Examples of this problem are scheduling the installation of point-of-sale terminals in supermarket and retail chains, and teller terminals in banks. We have formulated the installation scheduling problem ...

We discuss two families of valid inequalities for linear mixed integer programming problems with cone constraints of arbitrary order, which arise in the context of stochastic optimization with downside risk measures. In particular, we extend the results of Atamtürk and Narayanan (Math. Program., 2010, 2011), who developed mixed integer rounding cuts and lifted cuts for mixed integer programming...