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Coverings of convex bodies have emerged as a central component in the design of efficient solutions to approximation problems involving convex bodies. Intuitively, given a convex body $K$ and $\epsilon> 0$, a covering is a collection of…

Computational Geometry · Computer Science 2023-03-16 Sunil Arya , Guilherme D. da Fonseca , David M. Mount

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…

Data Structures and Algorithms · Computer Science 2024-11-26 Antonios Antoniadis , Marek Eliáš , Adam Polak , Moritz Venzin

Efficient algorithms for convex optimization, such as the ellipsoid method, require an a priori bound on the radius of a ball around the origin guaranteed to contain an optimal solution if one exists. For linear and convex quadratic…

Data Structures and Algorithms · Computer Science 2025-11-06 Lucas Slot , David Steurer , Manuel Wiedmer

We consider the problem of graph searching with prediction recently introduced by Banerjee et al. (2022). In this problem, an agent, starting at some vertex $r$ has to traverse a (potentially unknown) graph $G$ to find a hidden goal node…

Data Structures and Algorithms · Computer Science 2024-03-19 Adela Frances DePavia , Erasmo Tani , Ali Vakilian

Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…

Optimization and Control · Mathematics 2019-11-21 Cyrille W. Combettes , Sebastian Pokutta

Motivated by the success of Nesterov's accelerated gradient algorithm for convex minimization problems, we examine whether it is possible to achieve similar performance gains in the context of online learning in games. To that end, we…

Computer Science and Game Theory · Computer Science 2024-12-31 Kyriakos Lotidis , Angeliki Giannou , Panayotis Mertikopoulos , Nicholas Bambos

In 2001, K\'arolyi, Pach and T\'oth introduced a family of point sets to solve an Erd\H{o}s-Szekeres type problem; which have been used to solve several other Ed\H{o}s-Szekeres type problems. In this paper we refer to these sets as nested…

Computational Geometry · Computer Science 2016-06-09 Frank Duque , Ruy Fabila-Monroy , Carlos Hidalgo-Toscano , Pablo Pérez-Lantero

Constrained motion planning is a common but challenging problem in robotic manipulation. In recent years, data-driven constrained motion planning algorithms have shown impressive planning speed and success rate. Among them, the latent…

Robotics · Computer Science 2026-01-01 Jiawei Zhang , Chengchao Bai , Wei Pan , Tianhang Liu , Jifeng Guo

We describe an apparatus for subgradient-following of the optimum of convex problems with variational penalties. In this setting, we receive a sequence $y_i,\ldots,y_n$ and seek a smooth sequence $x_1,\ldots,x_n$. The smooth sequence needs…

Machine Learning · Computer Science 2025-04-11 Kai-Chia Mo , Shai Shalev-Shwartz , Nisæl Shártov

We study differentially private (DP) algorithms for stochastic convex optimization: the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. (2019)…

Machine Learning · Computer Science 2020-05-12 Vitaly Feldman , Tomer Koren , Kunal Talwar

The Team Orienteering Problem (TOP) is an NP-hard routing problem in which a fleet of identical vehicles aims at collecting rewards (prizes) available at given locations, while satisfying restrictions on the travel times. In TOP, each…

Data Structures and Algorithms · Computer Science 2020-01-06 Lucas Assunção , Geraldo Robson Mateus

We consider linear search for an escaping target whose speed and initial position are unknown to the searcher. A searcher (an autonomous mobile agent) is initially placed at the origin of the real line and can move with maximum speed $1$ in…

Discrete Mathematics · Computer Science 2024-04-24 Jared Coleman , Dmitry Ivanov , Evangelos Kranakis , Danny Krizanc , Oscar Morales-Ponce

One of the most popular approaches to multi-target tracking is tracking-by-detection. Current min-cost flow algorithms which solve the data association problem optimally have three main drawbacks: they are computationally expensive, they…

Computer Vision and Pattern Recognition · Computer Science 2014-12-30 Philip Lenz , Andreas Geiger , Raquel Urtasun

A game theory inspired methodology is proposed for finding a function's saddle points. While explicit descent methods are known to have severe convergence issues, implicit methods are natural in an adversarial setting, as they take the…

Optimization and Control · Mathematics 2019-06-04 Montacer Essid , Esteban Tabak , Giulio Trigila

With the development of robotics, there are growing needs for real time motion planning. However, due to obstacles in the environment, the planning problem is highly non-convex, which makes it difficult to achieve real time computation…

Optimization and Control · Mathematics 2018-05-22 Changliu Liu , Chung-Yen Lin , Masayoshi Tomizuka

Let $S$ be a set of $n$ points in $\mathbb{R}^d$. A Steiner convex partition is a tiling of ${\rm conv}(S)$ with empty convex bodies. For every integer $d$, we show that $S$ admits a Steiner convex partition with at most $\lceil…

Computational Geometry · Computer Science 2014-02-04 Adrian Dumitrescu , Sariel Har-Peled , Csaba D. Tóth

In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…

Data Structures and Algorithms · Computer Science 2025-04-30 Aditya Bhaskara , Sepideh Mahabadi , Madhusudhan Reddy Pittu , Ali Vakilian , David P. Woodruff

The trend in modern science and technology is to take vector measurements rather than scalars, ruthlessly scaling to ever higher dimensional vectors. For about two decades now, traditional scalar Compressed Sensing has been synonymous with…

Machine Learning · Computer Science 2025-05-02 Apratim Dey , David Donoho

This paper presents a Successive Convexification ($ \texttt{SCvx} $) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of non-convexity may include nonlinear dynamics and…

Optimization and Control · Mathematics 2017-10-23 Yuanqi Mao , Daniel Dueri , Michael Szmuk , Behçet Açıkmeşe

One of the oldest and richest problems from continuous location science is the famous Fermat-Torricelli problem, asking for the unique point in Euclidean space that has minimal distance sum to n given (non-collinear) points. Many natural…

Metric Geometry · Mathematics 2016-01-08 Thomas Jahn , Yaakov S. Kupitz , Horst Martini , Christian Richter