The Intentional Controlled Islanding (ICI) and the Black Start Allocation (BSA) are two examples of problems in the power systems literature that have been formulated as Mixed Integer Programs (MIPs). A key consideration in both of these problems is that each island must have at least one energized generator. In this paper, we provide three … Read more
In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming only the knowledge of the mean and the covariance matrix entries restricted to block-diagonal patterns, we develop a reduced semidefinite programming formulation, … Read more
We study cyclic binary strings with bounds on the lengths of the intervals of consecutive ones and zeros. This is motivated by scheduling problems where such binary strings can be used to represent the state (on/off) of a machine. In this context the bounds correspond to minimum and maximum lengths of on- or off-intervals, and … Read more
A 0/1 matrix has the Consecutive Ones Property if a permutation of its columns exists such that the ones appear consecutively in each row. In many applications, one has to find a matrix having the consecutive ones property and optimizing a linear objective function. For this problem, literature proposes, among other approaches, an Integer Linear … Read more
This paper studies extended formulations for radial cones at vertices of polyhedra, where the radial cone of a polyhedron P at a vertex v of P is the polyhedron defined by the constraints of P that are active at v. Given an extended formulation for P, it is easy to obtain an extended formulation of … Read more
The multilinear polytope MP_G of a hypergraph G is the convex hull of a set of binary points satisfying a collection of multilinear equations. We introduce the running-intersection inequalities, a new class of facet-defining inequalities for the multilinear polytope. Accordingly, we define a new polyhedral relaxation of MP_G referred to as the running-intersection relaxation and … Read more
We propose a combinatorial algorithm to compute the Hoffman constant of a system of linear equations and inequalities. The algorithm is based on a characterization of the Hoffman constant as the largest of a finite canonical collection of easy-to-compute Hoffman constants. Our algorithm and characterization extend to the more general context where some of the … Read more
In this paper, we study the class of linear and discrete optimization problems in which the objective coefficients are chosen randomly from a distribution, and the goal is to evaluate robust bounds on the expected optimal value as well as the marginal distribution of the optimal solution. The set of joint distributions is assumed to … Read more
We consider generalizations of parity polytopes whose variables, in addition to a parity constraint, satisfy certain ordering constraints. More precisely, the variable domain is partitioned into k contiguous groups, and within each group, we require the variables to be sorted nonincreasingly. Such constraints are used to break symmetry after replacing an integer variable by a … Read more
Making cut generating functions (CGFs) computationally viable is a central question in modern integer programming research. One would like to nd CGFs that are simultaneously good, i.e., there are good guarantees for the cutting planes they generate, and ecient, meaning that the values of the CGFs can be computed cheaply (with procedures that have some … Read more