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Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex…

Machine Learning · Computer Science 2023-06-21 Marin Ballu , Quentin Berthet

We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…

Computation · Statistics 2020-10-20 Lizhen Lin , Bayan Saparbayeva , Michael Minyi Zhang , David B. Dunson

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

Optimization and Control · Mathematics 2022-03-02 Boris S. Mordukhovich , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

While the search for quantum advantage typically focuses on speedups in execution time, quantum algorithms also offer the potential for advantage in space complexity. Previous work has shown such advantages for data stream problems, in…

Quantum Physics · Physics 2023-11-27 John Kallaugher , Ojas Parekh , Nadezhda Voronova

In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent…

Computer Science and Game Theory · Computer Science 2023-01-18 Volkan Cevher , Georgios Piliouras , Ryann Sim , Stratis Skoulakis

In the polytope membership problem, a convex polytope $K$ in $\mathbb{R}^d$ is given, and the objective is to preprocess $K$ into a data structure so that, given any query point $q \in \mathbb{R}^d$, it is possible to determine efficiently…

Computational Geometry · Computer Science 2018-01-11 Sunil Arya , Guilherme D. da Fonseca , David M. Mount

We present randomized algorithms that compute $(1+\epsilon)$-approximate minimum global edge and vertex cuts in weighted directed graphs in $O(\log^4(n) / \epsilon)$ and $O(\log^5(n)/\epsilon)$ single-commodity flows, respectively. With the…

Data Structures and Algorithms · Computer Science 2025-12-02 Kent Quanrud

We characterize the streaming space complexity of every symmetric norm $l$ (a norm on $\mathbb{R}^n$ invariant under sign-flips and coordinate-permutations), by relating this space complexity to the measure-concentration characteristics of…

Data Structures and Algorithms · Computer Science 2017-06-27 Jaroslaw Blasiok , Vladimir Braverman , Stephen R. Chestnut , Robert Krauthgamer , Lin F. Yang

We study algorithms for the sliding-window model, an important variant of the data-stream model, in which the goal is to compute some function of a fixed-length suffix of the stream. We extend the smooth-histogram framework of Braverman and…

Data Structures and Algorithms · Computer Science 2022-05-26 Robert Krauthgamer , David Reitblat

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…

Data Structures and Algorithms · Computer Science 2019-05-30 David Durfee , Yu Gao , Anup B. Rao , Sebastian Wild

We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational…

Machine Learning · Computer Science 2019-09-10 Ibrahim Jubran , Dan Feldman

A numerical method for an inverse problem for an elliptic equation with the running source at multiple positions is presented. This algorithm does not rely on a good first guess for the solution. The so-called "approximate global…

Mathematical Physics · Physics 2015-03-20 Jianzhong Su , Michael V. Klibanov , Yueming Liu , Zhijin Lin , Natee Pantong , Hanli Liu

We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be…

Data Structures and Algorithms · Computer Science 2021-02-15 Yanhao Wang , Francesco Fabbri , Michael Mathioudakis

The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…

Data Structures and Algorithms · Computer Science 2016-08-02 Michalis Kallitsis , Stilian Stoev , George Michailidis

We present a numerical algorithm for nonnegative matrix factorization (NMF) problems under noisy separability. An NMF problem under separability can be stated as one of finding all vertices of the convex hull of data points. The research…

Machine Learning · Statistics 2015-03-06 Tomohiko Mizutani

In the maximum independent set of convex polygons problem, we are given a set of $n$ convex polygons in the plane with the objective of selecting a maximum cardinality subset of non-overlapping polygons. Here we study a special case of the…

Computational Geometry · Computer Science 2024-02-13 Fabrizio Grandoni , Edin Husić , Mathieu Mari , Antoine Tinguely

Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…

Robotics · Computer Science 2022-03-16 Steve Tonneau

Diversity maximization is a fundamental problem with wide applications in data summarization, web search, and recommender systems. Given a set $X$ of $n$ elements, it asks to select a subset $S$ of $k \ll n$ elements with maximum…

Data Structures and Algorithms · Computer Science 2023-04-27 Yanhao Wang , Francesco Fabbri , Michael Mathioudakis

We present a near-optimal distributed algorithm for $(1+o(1))$-approximation of single-commodity maximum flow in undirected weighted networks that runs in $(D+ \sqrt{n})\cdot n^{o(1)}$ communication rounds in the \Congest model. Here, $n$…

Data Structures and Algorithms · Computer Science 2015-08-20 Mohsen Ghaffari , Andreas Karrenbauer , Fabian Kuhn , Christoph Lenzen , Boaz Patt-Shamir

In this work, we provide the first practical evaluation of the structural rounding framework for approximation algorithms. Structural rounding works by first editing to a well-structured class, efficiently solving the edited instance, and…

Data Structures and Algorithms · Computer Science 2019-11-04 Brian Lavallee , Hayley Russell , Blair D. Sullivan , Andrew van der Poel