Related papers: Sparse multi-term disjunctive cuts for the epigrap…
Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…
We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model (coarsened with respect to variables) and a coarse…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense…
The Vertex Separator Problem for a graph is to find the smallest collection of vertices whose removal breaks the graph into two disconnected subsets that satisfy specified size constraints. In the paper 10.1016/j.ejor.2014.05.042, the…
Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…
A randomized algorithm for finding sparse cuts is given which is based on constructing a dual markov chain called multiscale rings process(MRP) and a new concept of entropy. It is shown how the time to absorption of the dual process…
Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose…
In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and…
The Minimum Cost Multicut Problem (MP) is a popular way for obtaining a graph decomposition by optimizing binary edge labels over edge costs. While the formulation of a MP from independently estimated costs per edge is highly flexible and…
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…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…
Image segmentation is usually addressed by training a model for a fixed set of object classes. Incorporating additional classes or more complex queries later is expensive as it requires re-training the model on a dataset that encompasses…
We propose a Branch-and-Cut (B&C) method for solving general MAP-MRF inference problems. The core of our method is a very efficient bounding procedure, which combines scalable semidefinite programming (SDP) and a cutting-plane method for…
Given an undirected, edge-weighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimum-weight set of edges such that, after deleting these edges, the two terminals of each pair…
We introduce and study $\ell_p$-norm-multiway-cut: the input here is an undirected graph with non-negative edge weights along with $k$ terminals and the goal is to find a partition of the vertex set into $k$ parts each containing exactly…
DR-submodular functions encompass a broad class of functions which are generally non-convex and non-concave. We study the problem of minimizing any DR-submodular function, with continuous and general integer variables, under box constraints…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
There has been a surge of interest in learning optimal decision trees using mixed-integer programs (MIP) in recent years, as heuristic-based methods do not guarantee optimality and find it challenging to incorporate constraints that are…