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The stochastic $H^\infty$-norm is defined as the $L^2$-induced norm of the input-output operator of a stochastic linear system. Like the deterministic $H^\infty$-norm it is characterised by a version of the bounded real lemma, but without a…

Numerical Analysis · Mathematics 2017-03-14 Tobias Damm , Peter Benner , Jan Hauth

Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective…

Data Structures and Algorithms · Computer Science 2011-04-28 Michael W. Mahoney , Lorenzo Orecchia

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

Computer Vision and Pattern Recognition · Computer Science 2020-03-23 Huu Le , Christopher Zach

In this paper, a new computational method for the purpose of multimodal vibration mitigation using multiple tuned mass dampers is proposed. Classically, the minimization of the maximum amplitude is carried out using direct $H_\infty$…

Dynamical Systems · Mathematics 2021-02-26 Ghislain Raze , Gaetan Kerschen

This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…

Machine Learning · Computer Science 2024-09-20 Ronald Katende

This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…

Numerical Analysis · Mathematics 2022-02-17 Yuji Nakatsukasa , Joel A. Tropp

Gradient-based solvers risk convergence to local optima, leading to incorrect researcher inference. Heuristic-based algorithms are able to ``break free" of these local optima to eventually converge to the true global optimum. However, given…

Econometrics · Economics 2024-01-17 Zachary Porreca

We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…

Quantum Physics · Physics 2026-02-02 Simon Apers , Sander Gribling

Stochastic variance reduced optimization methods are known to be globally convergent while they suffer from slow local convergence, especially when moderate or high accuracy is needed. To alleviate this problem, we propose an optimization…

Optimization and Control · Mathematics 2021-11-15 Hamed Sadeghi , Pontus Giselsson

We consider frequency-weighted damping optimization for vibrating systems described by a second-order differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the…

Numerical Analysis · Mathematics 2021-04-12 Nevena Jakovcevic Stor , Tim Mitchell , Zoran Tomljanovic , Matea Ugrica

The continuous computational power growth in the last decades has made solving several optimization problems significant to humankind a tractable task; however, tackling some of them remains a challenge due to the overwhelming amount of…

Machine Learning · Computer Science 2023-02-01 Luiz C. F. Ribeiro , Mateus Roder , Gustavo H. de Rosa , Leandro A. Passos , João P. Papa

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

Optimization and Control · Mathematics 2016-02-29 Farbod Roosta-Khorasani , Michael W. Mahoney

We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound…

Machine Learning · Computer Science 2020-06-23 Andrew Wagenmaker , Kevin Jamieson

We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…

Quantum Physics · Physics 2026-03-18 Ahmet Burak Catli , Sophia Simon , Nathan Wiebe

We propose an iterative improvement method for the Harrow-Hassidim-Lloyd (HHL) algorithm to solve a linear system of equations. This is a quantum-classical hybrid algorithm. The accuracy is essential to solve the linear system of equations.…

Quantum Physics · Physics 2021-08-18 Yoshiyuki Saito , Xinwei Lee , Dongsheng Cai , Nobuyoshi Asai

The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…

Quantum Physics · Physics 2026-03-18 Dhruv Sood , Nilmani Mathur , Vikram Tripathi

We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale…

Analysis of PDEs · Mathematics 2020-05-27 Philippe Chartier , Mohammed Lemou , Léopold Trémant

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

We propose a fast method to approximate the real stability radius of a linear dynamical system with output feedback, where the perturbations are restricted to be real valued and bounded with respect to the Frobenius norm. Our work builds on…

Optimization and Control · Mathematics 2017-02-09 Nicola Guglielmi , Mert Gurbuzbalaban , Tim Mitchell , Michael Overton

We study novel robust zero-order algorithms with acceleration for the solution of real-time optimization problems. In particular, we propose a family of extremum seeking dynamics that can be universally modeled as singularly perturbed…

Optimization and Control · Mathematics 2020-12-17 Jorge I. Poveda , Na Li