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We study multivariate numerical integration of smooth functions in weighted Sobolev spaces with dominating mixed smoothness $\alpha\geq 2$ defined over the $s$-dimensional unit cube. We propose a new quasi-Monte Carlo (QMC)-based quadrature…
We study the complexity of approximating Wassertein barycenter of $m$ discrete measures, or histograms of size $n$ by contrasting two alternative approaches, both using entropic regularization. The first approach is based on the Iterative…
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
In the NP-hard \textsc{Group Closeness Centrality Maximization} problem, the input is a graph $G = (V,E)$ and a positive integer $k$, and the task is to find a set $S \subseteq V$ of size $k$ that maximizes the reciprocal of group farness…
Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear…
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…
Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for $k$-means with a provable guarantee is a simple…
Given a set ${\cal D}$ of unit disks in the Euclidean plane, we consider (i) the {\it discrete unit disk cover} (DUDC) problem and (ii) the {\it rectangular region cover} (RRC) problem. In the DUDC problem, for a given set ${\cal P}$ of…
Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and…
We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the…
In paper a new definition of reduced Pade approximant and algorithm for its computing is proposed. Our approach is based on the investigation of the kernel structure of the Toeplitz matrix. It is shown that the reduced Pade approximant…
Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems,…
This paper is devoted to the study of a problem of Cassels in multiplicative Diophantine approximation which involves minimising values of a product of affine linear forms computed at integral points. It was previously known that values of…
Covering and elimination inequalities are central to combinatorial optimization, yet their role has largely been studied in problem-specific settings or via no-good cuts. This paper introduces a unified perspective that treats these…
The Dowker complex $\mathrm{D}_{R}(X,Y)$ is a simplicial complex capturing the topological interplay between two finite sets $X$ and $Y$ under some relation $R\subseteq X\times Y$. While its definition is asymmetric, the famous Dowker…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
We suggest efficient and provable methods to compute an approximation for imbalanced point clustering, that is, fitting $k$-centers to a set of points in $\mathbb{R}^d$, for any $d,k\geq 1$. To this end, we utilize \emph{coresets}, which,…
Panoptic segmentation is a key enabler for robotic perception, as it unifies semantic understanding with object-level reasoning. However, the increasing complexity of state-of-the-art models makes them unsuitable for deployment on…