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This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…

Numerical Analysis · Mathematics 2025-01-14 Gouranga Mallik , Ramesh Chandra Sau

In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain…

Optimization and Control · Mathematics 2021-05-21 Nikita Doikov , Yurii Nesterov

Exponents and logarithms are fundamental components in many important applications such as logistic regression, maximum likelihood, relative entropy, and so on. Since the exponential cone can be viewed as the epigraph of perspective of the…

Optimization and Control · Mathematics 2022-03-22 Qing Ye , Weijun Xie

An optimal mesh size of the sampling region can help to reduce computational burden in practical applications. In this work, we investigate optimal choices of mesh sizes for the identifications of medium obstacles from either the far-field…

Numerical Analysis · Mathematics 2018-10-22 Habib Ammari , Yat Tin Chow , Keji Liu

An increasing number of machine learning tasks deal with learning representations from set-structured data. Solutions to these problems involve the composition of permutation-equivariant modules (e.g., self-attention, or individual…

Machine Learning · Computer Science 2021-03-09 Navid Naderializadeh , Soheil Kolouri , Joseph F. Comer , Reed W. Andrews , Heiko Hoffmann

The Two-dimensional Bin Packing Problem calls for packing a set of rectangular items into a minimal set of larger rectangular bins. Items must be packed with their edges parallel to the borders of the bins, cannot be rotated and cannot…

Optimization and Control · Mathematics 2019-09-17 Jean-François Côté , Mohamed Haouari , Manuel Iori

Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…

Statistics Theory · Mathematics 2007-06-13 Arthur Berg , Dimitris Politis

High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the…

Optimization and Control · Mathematics 2017-08-18 Xin Yee Lam , J. S. Marron , Defeng Sun , Kim-Chuan Toh

The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least…

Numerical Analysis · Mathematics 2015-06-02 Mike Espig , Wolfgang Hackbusch , Aram Khachatryan

Representing a polygon using a set of simple shapes has numerous applications in different use-case scenarios. We consider the problem of covering the interior of a rectilinear polygon with holes by a set of area-weighted, axis-aligned…

Computational Geometry · Computer Science 2023-12-15 Kathrin Hanauer , Martin P. Seybold , Julian Unterweger

The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…

Combinatorics · Mathematics 2011-04-07 Volker Kaibel

Every graph G can be embedded in a Euclidean space as a two-distance set. The Euclidean representation number of G is the smallest dimension in which G is representable by such an embedding. We consider spherical and J-spherical…

Metric Geometry · Mathematics 2019-06-26 Oleg R. Musin

We derive the optimal second-order coding region and moderate deviations constant for successive refinement source coding with a joint excess-distortion probability constraint. We consider two scenarios: (i) a discrete memoryless source…

Information Theory · Computer Science 2016-08-29 Lin Zhou , Vincent Y. F. Tan , Mehul Motani

For a graph $G$ and a positive integer $c$, let $M_c(G)$ be the size of a subgraph of $G$ induced by a randomly sampled subset of $c$ vertices. Second-order moments of $M_c(G)$ encode part of the structure of $G$. We use this fact, coupled…

Combinatorics · Mathematics 2023-04-25 Nicola Apollonio

We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…

Computational Geometry · Computer Science 2011-12-01 Alina Ene , Sariel Har-Peled , Benjamin Raichel

In projection-based model order reduction, a reduced-order approximation of the original full-order system is obtained by projecting it onto a reduced subspace that contains its dominant characteristics. The problem of frequency-weighted…

Systems and Control · Electrical Eng. & Systems 2021-05-04 Umair Zulfiqar , Victor Sreeram , Mian Ilyas Ahmad , Xin Du

We introduce and study Minimum Cut Representability, a framework to solve optimization and feasibility problems over stable matchings by representing them as minimum s-t cut problems on digraphs over rotations. We provide necessary and…

Optimization and Control · Mathematics 2025-04-08 Yuri Faenza , Ayoub Foussoul , Chengyue He

For the numerical solution of shape optimization problems, particularly those constrained by partial differential equations (PDEs), the quality of the underlying mesh is of utmost importance. Particularly when investigating complex…

Optimization and Control · Mathematics 2025-10-14 Sebastian Blauth , Christian Leithäuser

A large number matrix optimization problems are described by orthogonally invariant norms. This paper is devoted to the study of variational analysis of the orthogonally invariant norm cone of symmetric matrices. For a general orthogonally…

Optimization and Control · Mathematics 2023-02-14 Yule Zhang , Jihong Zhang , Liwei Zhang

We consider polyhedral cones, associated with quasi-semi-metrics (oriented distances), in particular, with oriented multi-cuts, on n points. We computed the number of facets and of extreme rays, their adjacencies, and incidences of the…

Metric Geometry · Mathematics 2007-05-23 M. Deza , M. Dutour , E. Panteleeva