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In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous…

Optimization and Control · Mathematics 2021-07-27 Jingjing Fan , Bing Tan , Songxiao Li

In this paper we consider a dual gradient method for solving linear ill-posed problems $Ax = y$, where $A : X \to Y$ is a bounded linear operator from a Banach space $X$ to a Hilbert space $Y$. A strongly convex penalty function is used in…

Numerical Analysis · Mathematics 2022-06-16 Qinian Jin

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…

Machine Learning · Statistics 2022-07-18 Junhong Lin , Alessandro Rudi , Lorenzo Rosasco , Volkan Cevher

In this work, we have abstractly generalized the similarity law for multidimensional vectors. Initially, the law of similarity was derived for one-dimensional vectors. Although it operated with such values of the ratio of parts of the…

General Mathematics · Mathematics 2025-01-14 Artyom M. Grigoryan , Meruzhan M. Grigoryan

Many recently proposed gradient projection algorithms with inertial extrapolation step for solving quasi-variational inequalities in Hilbert spaces are proven to be strongly convergent with no linear rate given when the cost operator is…

Optimization and Control · Mathematics 2024-04-23 Yonghong Yao , Lateef O. Jolaoso , Yekini Shehu

Based on a comparison principle, we derive an exponential rate of convergence for solutions to the initial-boundary value problem for a class of quasilinear parabolic equations in one space dimension. We then apply the result to some models…

Analysis of PDEs · Mathematics 2016-12-19 Seonghak Kim

The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…

Optimization and Control · Mathematics 2015-10-30 Dang Van Hieu

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence…

Optimization and Control · Mathematics 2021-12-28 Mostafa Ghadampour , Ebrahim Soori , Ravi P. Agarwal , Donal O'Regan

In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded H\"older regularity assumption which generalizes the…

Optimization and Control · Mathematics 2018-08-16 Jonathan M. Borwein , Guoyin Li , Matthew K. Tam

Efficient global optimization is the problem of minimizing an unknown function f, using as few evaluations f(x) as possible. It can be considered as a continuum-armed bandit problem, with noiseless data and simple regret. Expected…

Machine Learning · Statistics 2013-02-19 Adam D. Bull

Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…

Statistics Theory · Mathematics 2024-12-12 Naveen Gupta , S. Sivananthan , Bharath K. Sriperumbudur

We prove some results on the rate of convergence of greedy algorithms, which provide expansions. We consider both the case of Hilbert spaces and the more general case of Banach spaces. The new ingredient of the paper is that we bound the…

Numerical Analysis · Mathematics 2023-04-14 V. N. Temlyakov

The golden ratio and Fibonacci numbers are found to occur in various aspects of nature. We discuss the occurrence of this ratio in an interesting physical problem concerning center of masses in two dimensions. The result is shown to be…

General Mathematics · Mathematics 2020-03-16 Gautam Dutta , Mitaxi Mehta , Praveen Pathak

We analyze the convergence of the harmonic balance method for computing isolated periodic solutions of a large class of continuously differentiable Hilbert space valued differential-algebraic equations (DAEs). We establish asymptotic…

Numerical Analysis · Mathematics 2021-11-25 Andrew Steyer , Robert J. Kuether

We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special…

Numerical Analysis · Mathematics 2007-05-23 Abdenasser Benahmed

We establish some results for the rate of convergence in total variation of a Gibbs sampler to its equilibrium distribution. This sampler is motivated by a hierarchical Bayesian inference construction for a gamma random variable. Our…

Probability · Mathematics 2014-12-08 Oliver Jovanovski , Neal Madras

In the present work we show how different ways to solve biquadratic equations can lead us to different representations of its solutions. A particular equation which has the golden ratio and its reciprocal as solutions is shown as an…

General Mathematics · Mathematics 2014-12-25 Leonardo Mondaini

We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure…

Machine Learning · Computer Science 2019-09-09 Harikrishna Narasimhan , Andrew Cotter , Maya Gupta

In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate…

Machine Learning · Statistics 2025-09-18 Marat Khusainov , Marina Sheshukova , Alain Durmus , Sergey Samsonov

Inspired by the adaptive Golden Ratio Algorithm (aGRAAL), we propose two new methods for solving monotone variational inequalities. We show that by selecting the momentum parameter beyond the golden ratio in aGRAAL, the convergence speed…

Optimization and Control · Mathematics 2026-04-07 Reza Rahimi Baghbadorani , Peyman Mohajerin Esfahani , Sergio Grammatico