Related papers: Efficient solutions for weight-balanced partitioni…

In the maximum constraint satisfaction problem (MAX CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given finite domain to the variables so…

In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…

In this paper we consider a general problem set-up for a wide class of convex and robust distributed optimization problems in peer-to-peer networks. In this set-up convex constraint sets are distributed to the network processors who have to…

Common clustering methods, such as $k$-means and convex clustering, group similar vector-valued observations into clusters. However, with the increasing prevalence of matrix-valued observations, which often exhibit low rank characteristics,…

Distributed signal processing for wireless sensor networks enables that different devices cooperate to solve different signal processing tasks. A crucial first step is to answer the question: who observes what? Recently, several distributed…

Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…

The method of Hol\'y, Sokol and \v{C}ern\'y (Applied Soft Computing, 2017, Vol. 60, p. 752-762) clusters objects based on their incidence in a large number of given sets. The idea is to minimize the occurrence of multiple objects from the…

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…

Convex optimization with equality and inequality constraints is a ubiquitous problem in several optimization and control problems in large-scale systems. Recently there has been a lot of interest in establishing accelerated convergence of…

Constrained clustering is a semi-supervised task that employs a limited amount of labelled data, formulated as constraints, to incorporate domain-specific knowledge and to significantly improve clustering accuracy. Previous work has…

In this article we study a broad class of integer programming problems in variable dimension. We show that these so-termed {\em n-fold integer programming problems} are polynomial time solvable. Our proof involves two heavy ingredients…

This paper presents a novel geometrical approach to investigate the convexity of a density-based cluster. Our approach is grid-based and we are about to calibrate the value space of the cluster. However, the cluster objects are coming from…

This work concerns an alignment problem that has applications in many geospatial problems such as resource allocation and building reliable disease maps. Here, we introduce the problem of optimally aligning $k$ collections of $m$ spatial…

As the data size in Machine Learning fields grows exponentially, it is inevitable to accelerate the computation by utilizing the ever-growing large number of available cores provided by high-performance computing hardware. However, existing…

Efficient exact algorithms for Discrete Optimization (DO) rely heavily on strong primal and dual bounds. Relaxed Decision Diagrams (DDs) provide a versatile mechanism for deriving such dual bounds by compactly over-approximating the…

The task of clustering a set of objects based on multiple sources of data arises in several modern applications. We propose an integrative statistical model that permits a separate clustering of the objects for each data source. These…

Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the…

We address the problem of clustering a set of points in $\mathbb{R}^d$ with axis-parallel clusters. Previous exact approaches to this problem are mostly based on integer programming formulations and can only solve to optimality instances of…

The analysis of large datasets is often complicated by the presence of missing entries, mainly because most of the current machine learning algorithms are designed to work with full data. The main focus of this work is to introduce a…

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…