Related papers: Intersection Cuts for Nonlinear Integer Programmin…
In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…
Many applications require solving sequences of related mixed-integer linear programs. We introduce a class of parametric disjunctive inequalities (PDIs), obtained by reusing the disjunctive proofs of optimality from prior solves to…
We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous…
Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
Prune-and-search is an important paradigm for solving many important geometric problems. We show that the general prune-and-search technique can be implemented where the objects are given in read-only memory. As examples we consider…
This paper proposes a Mixed-Integer Linear Programming approach for the Soft Graph Clustering Problem. This is the first method that simultaneously allocates membership proportion for vertices that lie in multiple clusters, and that…
Vertex splitting is a graph modification operation in which a vertex is replaced by multiple vertices such that the union of their neighborhoods equals the neighborhood of the original vertex. We introduce and study vertex splitting as a…
This paper proposes a mixed-integer nonlinear programming approach for joint scheduling of long-term maintenance decisions and short-term production for groups of complex machines with multiple interacting components. We introduce an…
We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a…
We consider mixed integer linear programs where free integer variables are expressed in terms of nonnegative continuous variables. When this model only has two integer variables, Dey and Louveaux characterized the intersection cuts that…
The partitioning of a system model will condition the structure of the controller as well as its design. In order to partition a system model, one has to know what states and inputs to group together to define subsystem models. For a given…
We present a geometrical analysis on the completely positive programming reformulation of quadratic optimization problems and its extension to polynomial optimization problems with a class of geometrically defined nonconvex conic programs…
In this paper, we cope with the following problem: compute the size of the convex hull of a configuration C, where the given data is the number of separating lines between any two points of the configuration (where the lines are generated…
Balas introduced disjunctive cuts in the 1970s for mixed-integer linear programs. Several recent papers have attempted to extend this work to mixed-integer conic programs. In this paper we study the structure of the convex hull of a…
For convex sets $K$ and $L$ in ${\mathbb{R}}^d$ we define $R_L(K)$ to be the convex hull of all points belonging to $K$ but not to the interior of $L$. Cutting-plane methods from integer and mixed-integer optimization can be expressed in…
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.
In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…