Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints C on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and a constraint is chosen from C also uniformly at random. This procedure is repeated m times independently. We ask the following question: is the resulting li...

We consider the rooted delay-constrained Steiner tree problem which arises for example in the design of centralized multicasting networks where quality of service constraints are of concern. We present a path based integer linear programming formulation which has already been considered in the literature for the spanning tree variant. Solving its linear relaxation by column generation has so fa...

Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results either rely on computing sparse eigenvalues of the design matrix or on properties of its nullspace. So far, no tractable algorithm is known to test these conditions and most current results rely ...

We describe a procedure to reduce variable bounds in Mixed Integer Nonlinear Programming (MINLP) as well as Mixed Integer Linear Programming (MILP) problems. The procedure works by combining pairs of inequalities of a linear programming (LP) relaxation of the problem. This bound reduction technique extends the feasibility based bound reduction technique on linear functions, used in MINLP and MI...

A special ordered set approach for optimizing a discontinuous separable piecewise linear function, This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its fin...

This paper is concerned with completely positive and semidefinite relaxations of quadratic programs with linear constraints and binary variables as presented in Burer [2]. It observes that all constraints of the relaxation associated with linear constraints of the original problem can be accumulated in a single linear constraint without changing the feasible set of either the completely positiv...

This paper studies an extended trust region subproblem (eTRS) in which the trust region intersects the unit ball with m linear inequality constraints. When m = 0, m = 1, or m = 2 and the linear constraints are parallel, it is known that the eTRS optimal value equals the optimal value of a particular convex relaxation, which is solvable in polynomial time. However, it is also known that, when m ...

Correlation clustering is an exciting area of research in the fields of graphical models and image segmentation. In this article we study the linear programming (LP) relaxation corresponding to PlanarCC and the multi-cut LP relaxation which are two methods for correlation clustering. We demonstrate that they have equal value when optimized. This provides justification for the use of PlanarCC wh...

In this note, we show that the linear programming for computing the quasi-additive bound of the formula size of a Boolean function presented by Ueno [MFCS’10] is equivalent to the dual problem of the linear programming relaxation of an integer programming for computing the protocol partition number. Together with the result of Ueno [MFCS’10], our results imply that there exists no gap between o...

In this paper we consider a semi-infinite relaxation of mixed integer linear programs. We show that minimal valid inequalities for this relaxation correspond to maximal latticefree convex sets, and that they arise from nonnegative, piecewise linear, positively homogeneous, convex functions.