Related papers: Another pedagogy for mixed-integer Gomory
Solving a polynomial system, or computing an associated Gr\"obner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the…
Cutting planes (cuts) are crucial for solving Mixed Integer Linear Programming (MILP) problems. Advanced MILP solvers typically rely on manually designed heuristic algorithms for cut selection, which require much expert experience and…
We develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning models. To accurately estimate MI from a finite number of samples, we present GMM-MI…
Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous…
The cutting stock problem with binary patterns (0-1 CSP) is a variant of CSP that usually appears as a relaxation of 2D and 3D packing problems. We present an exact method, based on an arc-flow formulation with side constraints, for solving…
Generalized additive index models (GAIMs) offer a flexible semiparametric framework for capturing complex data relationships, balancing the interpretability of parametric models with the flexibility of nonparametric approaches. However,…
Multivariate decision trees are powerful machine learning tools for classification and regression that attract many researchers and industry professionals. An optimal binary tree has two types of vertices, (i) branching vertices which have…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Mixed Integer Optimization has been a topic of active research in past decades. It has been used to solve Statistical problems of classification and regression involving massive data. However, there is an inherent degree of vagueness…
We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may…
Several novel mixed-integer linear and bilinear formulations are proposed for the optimum communication spanning tree problem. They implement the distance-based approach: graph distances are directly modeled by continuous, integral, or…
There has been a recent interest in cutting planes generated from two or more rows of the optimal simplex tableau. One can construct examples of integer programs for which a single cutting plane generated from two rows dominates the entire…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
The primal-dual column generation method (PDCGM) is a general-purpose column generation technique that relies on the primal-dual interior point method to solve the restricted master problems. The use of this interior point method variant…
Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear…
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of…
We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…
We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the…
This paper explores reoptimization techniques for solving sequences of similar mixed integer programs (MIPs) more effectively. Traditionally, these MIPs are solved independently, without capitalizing on information from previously solved…