Related papers: MIP and Set Covering approaches for Sparse Approxi…
Current state-of-the-art solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. However, for many real-world use cases, problem instances come from a narrow distribution. This has…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
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…
The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an…
The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
Many problems of interest in computer vision can be formulated as a problem of finding consistent correspondences between two feature sets. Feature correspondence (matching) problem with one-to-one mapping constraint is usually formulated…
In this paper, we consider the problem of compressed sensing where the goal is to recover almost all the sparse vectors using a small number of fixed linear measurements. For this problem, we propose a novel partial hard-thresholding…
We propose a Multi-step Screening Procedure (MSP) for the recovery of sparse linear models in high-dimensional data. This method is based on a repeated small penalty strategy that quickly converges to an estimate within a few iterations.…
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We study integer linear programs (ILP) of the form $\min\{c^\top x\ \vert\ Ax=b,l\le x\le u,x\in\mathbb Z^n\}$ and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…
We introduce the integrality number of an integer program (IP) in inequality form. Roughly speaking, the integrality number is the smallest number of integer constraints needed to solve an IP via a mixed integer (MIP) relaxation. One…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
We present a Mixed Integer Linear Program (MILP) approach in order to model the nonlinear problem of minimizing the tire noise. We first take more industrial constraints into account than in a former work of the authors. Then, we associate…
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in…