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AAA rational approximation has normally been carried out on a discrete set, typically hundreds or thousands of points in a real interval or complex domain. Here we introduce a continuum AAA algorithm that discretizes a domain adaptively as…

Numerical Analysis · Mathematics 2023-05-08 Toby Driscoll , Yuji Nakatsukasa , Lloyd N. Trefethen

The adaptive Antoulas-Anderson (AAA) algorithm for rational approximation is a widely used method for the efficient construction of highly accurate rational approximations to given data. While AAA can often produce rational approximations…

Numerical Analysis · Mathematics 2026-01-28 Michael S. Ackermann , Linus Balicki , Serkan Gugercin , Steffen W. R. Werner

Quadratic programs arise in robotics, communications, smart grids, and many other applications. As these problems grow in size, finding solutions becomes more computationally demanding, and new algorithms are needed to efficiently solve…

Optimization and Control · Mathematics 2020-06-17 Matthew Ubl , Matthew T. Hale

In many applications of autonomous mobile robots the following problem is encountered. Two maps of the same environment are available, one a prior map and the other a sensor map built by the robot. To benefit from all available information…

Robotics · Computer Science 2018-07-03 Saeed Gholami Shahbandi , Martin Magnusson

The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…

Information Theory · Computer Science 2010-08-24 Urs Niesen , Devavrat Shah , Gregory Wornell

We propose a Projected Proximal Point Algorithm (ProPPA) for solving a class of optimization problems. The algorithm iteratively computes the proximal point of the last estimated solution projected into an affine space which itself is…

Machine Learning · Computer Science 2015-03-20 Ranch Y. Q. Lai , Pong C. Yuen

In this paper we deploy for the first time Reinforcement-Learning algorithms in the context of the conformal-bootstrap programme to obtain numerical solutions of conformal field theories (CFTs). As an illustration, we use a soft…

High Energy Physics - Theory · Physics 2022-02-02 Gergely Kántor , Vasilis Niarchos , Constantinos Papageorgakis

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

Numerical Analysis · Computer Science 2017-02-15 Roberto Mínguez , Víctor Casero-Alonso

We investigate the proximal point algorithm (PPA) and its inexact extensions under an error bound condition, which guarantees a global linear convergence if the proximal regularization parameter is larger than the error bound condition…

Optimization and Control · Mathematics 2021-02-26 Meng Lu , Zheng Qu

Robust PCA has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bio-informatics, statistics, and machine learning to image and video processing in computer vision. Robust PCA…

Optimization and Control · Mathematics 2018-06-12 Shiqian Ma , Necdet Serhat Aybat

The rapidly changing landscapes of modern optimization problems require algorithms that can be adapted in real-time. This paper introduces an Adaptive Metaheuristic Framework (AMF) designed for dynamic environments. It is capable of…

Artificial Intelligence · Computer Science 2024-04-19 Bestoun S. Ahmed

A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various…

Computational Complexity · Computer Science 2007-07-04 Peter Gaži , Branislav Rovan

Rational minimax approximation of real functions on real intervals is an established topic, but when it comes to complex functions or domains, there appear to be no algorithms currently in use. Such a method is introduced here, the {\em…

Numerical Analysis · Mathematics 2019-08-19 Yuji Nakatsukasa , Lloyd N. Trefethen

A selection of algorithms for the rational approximation of matrix-valued functions are discussed, including variants of the interpolatory AAA method, the RKFIT method based on approximate least squares fitting, vector fitting, and a method…

Numerical Analysis · Mathematics 2021-04-21 Ion Victor Gosea , Stefan Güttel

Alignment of large language models remains a central challenge in natural language processing. Preference optimization has emerged as a popular and effective method for improving alignment, typically through training-time or prompt-based…

Machine Learning · Computer Science 2025-10-01 Frédéric Berdoz , Luca A. Lanzendörfer , René Caky , Roger Wattenhofer

We present a novel area matching algorithm for merging two different 2D grid maps. There are many approaches to address this problem, nevertheless, most previous work is built on some assumptions, such as rigid transformation, or similar…

Robotics · Computer Science 2019-11-19 Jiawei Hou , Haofei Kuang , Sören Schwertfeger

Current algorithms used to put a lattice gauge configuration into Landau gauge either suffer from the problem of critical slowing-down or involve an additional computational expense to overcome it. Evolutionary Algorithms (EAs), which have…

High Energy Physics - Lattice · Physics 2009-10-31 J. F. Markham , T. D. Kieu

Optimization is a critical tool for addressing a broad range of human and technical problems. However, the paradox of advanced optimization techniques is that they have maximum utility for problems in which the relationship between the…

Computational Engineering, Finance, and Science · Computer Science 2024-03-04 Hazhir Aliahmadi , Ruben Perez , Greg van Anders

Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…

Optimization and Control · Mathematics 2018-02-28 Cong Fang , Yameng Huang , Zhouchen Lin

The paper addresses the problem of optimizing a class of composite functions on Riemannian manifolds and a new first order optimization algorithm (FOA) with a fast convergence rate is proposed. Through the theoretical analysis for FOA, it…

Numerical Analysis · Computer Science 2015-12-08 Haoran Chen , Yanfeng Sun , Junbin Gao , Yongli Hu