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A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…

Numerical Analysis · Mathematics 2017-11-06 Enrico Bertolazzi , Marco Frego

The gradients used to train neural networks are typically computed using backpropagation. While an efficient way to obtain exact gradients, backpropagation is computationally expensive, hinders parallelization, and is biologically…

Machine Learning · Computer Science 2026-01-14 Katharina Flügel , Daniel Coquelin , Marie Weiel , Charlotte Debus , Achim Streit , Markus Götz

In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…

Optimization and Control · Mathematics 2021-11-03 Marko Nonhoff , Matthias A. Müller

Sketched gradient algorithms have been recently introduced for efficiently solving the large-scale constrained Least-squares regressions. In this paper we provide novel convergence analysis for the basic method {\it Gradient Projection…

Optimization and Control · Mathematics 2017-06-05 Junqi Tang , Mohammad Golbabaee , Mike Davies

We develop an algorithm that combines model-based and model-free methods for solving a nonlinear optimal control problem with a quadratic cost in which the system model is given by a linear state-space model with a small additive nonlinear…

Optimization and Control · Mathematics 2022-03-23 Yansong Li , Shuo Han

Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in machine learning. Reasons for this include its simplicity, speed and stability, as well as its competitive performance on $\ell_1$…

Machine Learning · Computer Science 2015-03-17 Ankan Saha , Ambuj Tewari

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the…

Quantum Physics · Physics 2024-08-27 Zhiyan Ding , Taehee Ko , Jiahao Yao , Lin Lin , Xiantao Li

This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…

Numerical Analysis · Mathematics 2024-06-11 Dongping Li , Xue Wang , Xiuying Zhang

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…

Quantum Physics · Physics 2018-08-20 Patrick Rebentrost , Maria Schuld , Leonard Wossnig , Francesco Petruccione , Seth Lloyd

An algorithm is presented for numerical computation of choreographies in the plane in a Newtonian potential and on the sphere in a cotangent potential. It is based on stereographic projection, approximation by trigonometric polynomials, and…

Numerical Analysis · Mathematics 2015-11-19 Hadrien Montanelli , Nikola Ivanov Gushterov

A landmark result of non-smooth convex optimization is that gradient descent is an optimal algorithm whenever the number of computed gradients is smaller than the dimension $d$. In this paper we study the extension of this result to the…

Optimization and Control · Mathematics 2021-01-15 Sébastien Bubeck , Qijia Jiang , Yin Tat Lee , Yuanzhi Li , Aaron Sidford

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…

Symbolic Computation · Computer Science 2011-04-06 Changbo Chen , Marc Moreno Maza

Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use…

Quantum Physics · Physics 2024-12-24 Vignesh Anantharamakrishnan , Márcio M. Taddei

Gradient descent is the method of choice for training large artificial intelligence systems. As these systems become larger, a better understanding of the mechanisms behind gradient training would allow us to alleviate compute costs and…

Machine Learning · Computer Science 2025-01-07 Ambroise Odonnat , Wassim Bouaziz , Vivien Cabannes

We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…

Optimization and Control · Mathematics 2023-07-10 Ryota Nozawa , Pierre-Louis Poirion , Akiko Takeda

Using an evolutionary algorithm combined with a gradient descent method we design optical cavities with significantly enhanced strong coupling rates between cavity photons and a single quantum emitter. Our approach allows us to find…

Optics · Physics 2022-07-27 D. V. Karpov , P. Horak

We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…

Optimization and Control · Mathematics 2022-02-15 Haixiang Zhang , Zeyu Zheng , Javad Lavaei

In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the…

Optimization and Control · Mathematics 2022-06-02 Wang Chen , Xinmin Yang , Yong Zhao

We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages,…

Optics · Physics 2009-11-13 Svenja Ettl , Jürgen Kaminski , Markus C. Knauer , Gerd Häusler

This paper introduces a circle detection method based on Differential Evolution (DE) optimization. Just as circle detection has been lately considered as a fundamental component for many computer vision algorithms, DE has evolved as a…

Computer Vision and Pattern Recognition · Computer Science 2014-05-30 Erik Cuevas , Daniel Zaldivar , Marco Perez , Marte Ramirez