Related papers: An extension of disjunctive programming and its im…
We study the mixed-integer epigraph of a special class of convex functions with non-convex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are…
We address the issue of generating cutting planes for mixed integer programs from multiple rows of the simplex tableau with the tools of disjunctive programming. A cut from q rows of the simplex tableau is an intersection cuts from a…
We introduce $\mathcal{V}$-polyhedral disjunctive cuts (VPCs) for generating valid inequalities from general disjunctions. Cuts are critical to integer programming solvers, but the benefit from many families is only realized when the cuts…
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…
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…
Optimization problems with discrete-continuous decisions are traditionally modeled in algebraic form via (non)linear mixed-integer programming. A more systematic approach to modeling such systems is to use Generalized Disjunctive…
Disjunctive cutting planes can tighten a relaxation of a mixed-integer linear program. Traditionally, such cuts are obtained by solving a higher-dimensional linear program, whose additional variables cause the procedure to be…
The cutting-plane approach to integer programming was initiated more that 40 years ago: Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau form and Balas introduced intersection cuts for the corner…
An important problem in optimization is the construction of mixed-integer programming (MIP) formulations of disjunctive constraints that are both strong and small. Motivated by lower bounds on the number of integer variables that are…
In this paper we propose a framework for combining Disjunctive Logic Programming and Poole's Probabilistic Horn Abduction. We use the concept of hypothesis to specify the probability structure. We consider the case in which probabilistic…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by…
The aims of this article are two-fold. First, we give a geometric characterization of the optimal basic solutions of the general linear programming problem (no compactness assumptions) and provide a simple, self-contained proof of it…
We investigate a canonical extension of a conventional combinatorial notion of reduced divisors to a notion of tropical projections, which can be defined as the unique minimizers of the so-called $B$-pseudonorms with respect to compact…
Reductions combine collections of input values with an associative and often commutative operator to produce collections of results. When the same input value contributes to multiple outputs, there is an opportunity to reuse partial…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
In this paper we develop a combinatorial abstraction of tropical linear programming. This generalizes the search for a feasible point of a system of min-plus-inequalities. It is based on the polyhedral properties of triangulations of the…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
A Reduction -- an accumulation over a set of values, using an associative and commutative operator -- is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…