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
With the advent of modern communications systems, much attention has been put on developing methods for securely transferring information between constituents of wireless sensor networks. To this effect, we introduce a mathematical programming formulation for the key management problem, which broadly serves as a mechanism for encrypting communications. In particular, an integer programming model of … Read more
In this paper, we consider polytopes P that are contained in the unit hypercube. We provide conditions on the set of 0,1 vectors not contained in P that guarantee that P has a small Chvatal rank. Our conditions are in terms of the subgraph induced by these infeasible 0,1 vertices in the skeleton graph of … Read more
Split cuts are prominent general-purpose cutting planes in integer programming. The split closure of a rational polyhedron is what is obtained after intersecting the half-spaces defined by all the split cuts for the polyhedron. In this paper, we prove that deciding whether the split closure of a rational polytope is empty is NP-hard, even when … Read more
We introduce two-stage distributionally robust disjunctive programs (TSDR-DPs) with disjunctive constraints in both stages and a general ambiguity set for the probability distributions. The TSDR-DPs subsume various classes of two-stage distributionally robust programs where the second stage problems are non-convex programs (such as mixed binary programs, semi-continuous program, nonconvex quadratic programs, separable non-linear programs, etc.). … Read more
We consider an extended version of the classical Max-k-Cut problem in which we additionally require that the parts of the graph partition are connected. For this problem we study two alternative mixed-integer linear formulations and review existing as well as develop new branch-and-cut techniques like cuts, branching rules, propagation, primal heuristics, and symmetry breaking. The … Read more
We consider a multi-player optimization where each player has her own optimization problem and the individual problems are connected by a cardinality constraint on their shared resources. We give distributed algorithms that allow each player to solve their own optimization problem and still achieve a global optimization solution for problems that possess a concavity property. … Read more