The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and has become … Read more
A need for an optimal solution for a given mathematical model is well known and many solution approaches have been developed to identify efficiently an optimal solution in a given situation. For example, one such class of mathematical models with industrial applications have been classified as mathematical programming models (MPM). The main idea behind these … Read more
The development of practically well-behaving integer programming formulations is an important aspect of solving linear optimization problems over a set $X \subseteq \{0,1\}^n$. In practice, one is often interested in strong integer formulations with additional properties, e.g., bounded coefficients to avoid numerical instabilities. This article presents a lower bound on the size of coefficients in … Read more
Recently, several classes of cutting planes have been introduced for binary polynomial optimization. In this paper, we present the first results connecting the combinatorial structure of these inequalities with their Chvatal rank. We show that almost all known cutting planes have Chvatal rank 1. All these inequalities have an associated hypergraph that is beta-acyclic, thus, … Read more
The field of Combinatorial Optimization (CO) is one of the most important areas in the general field of optimization, with important applications found in every industry, including both the private and public sectors. It is also one of the most active research areas pursued by the research communities of Operations Research, Computer Science, and Analytics … Read more
We consider combinatorial optimization problems with uncertainty in the cost vector. Recently a novel approach was developed to deal such uncertainties: instead of a single one robust solution, obtained by solving a min max problem, the authors consider a set of solutions obtained by solving a min max min problem. In this new approach the … Read more
The influence maximization problem (IMP) aims to determine the most influential individuals within a social network. In this study first we develop a binary integer program that approximates the original problem by Monte Carlo sampling. Next, to solve IMP efficiently, we propose a linear programming relaxation based method with a provable worst case bound that … Read more
Principal component analysis (PCA) is one of the most widely used dimensionality reduction tools in scientific data analysis. The PCA direction, given by the leading eigenvector of a covariance matrix, is a linear combination of all features with nonzero loadings—this impedes interpretability. Sparse principal component analysis (SPCA) is a framework that enhances interpretability by incorporating … Read more
We consider the problem of estimating the parameters of a multivariate Gaussian mixture model (GMM) given access to $n$ samples $\x_1,\x_2,\ldots ,\x_n \in\mathbb{R}^d$ that are believed to have come from a mixture of multiple subpopulations. State-of-the-art algorithms used to recover these parameters use heuristics to either maximize the log-likelihood of the sample or try to … Read more
We study cyclic binary strings with bounds on the lengths of the intervals of consecutive ones and zeros. This is motivated by scheduling problems where such binary strings can be used to represent the state (on/off) of a machine. In this context the bounds correspond to minimum and maximum lengths of on- or off-intervals, and … Read more