Results 31 to 40 of about 386,320 (315)
Mathematics, 2022 The main aim of this paper is twofold. Our first objective is to study a new system of generalized multivalued variational-like inequalities in Banach spaces and to establish its equivalence with a system of fixed point problems utilizing the concept of ...
Javad Balooee +3 more
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Hermite Fitted Block Integrator for Solving Second-Order Anisotropic Elliptic Type PDEs
Fractal and Fractional, 2022 A Hermite fitted block integrator (HFBI) for numerically solving second-order anisotropic elliptic partial differential equations (PDEs) was developed, analyzed, and implemented in this study.
Emmanuel Oluseye Adeyefa +3 more
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An Extended Gradient Method for Smooth and Strongly Convex Functions
Mathematics, 2023 In this work, we introduce an extended gradient method that employs the gradients of the preceding two iterates to construct the search direction for the purpose of solving the centralized and decentralized smooth and strongly convex functions ...
Xuexue Zhang, Sanyang Liu, Nannan Zhao
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Mathematics, 2022 Based on a successive convex programming method, an alternating iteration algorithm is proposed for solving a parameter-dependent distributionally robust optimization. Under the Slater-type condition, the convergence analysis of the algorithm is obtained.
Shuang Lin, Jie Zhang, Nan Shi
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On the Convergence Analysis of Muon
CoRRThe majority of parameters in neural networks are naturally represented as matrices. However, most commonly used optimizers treat these matrix parameters as flattened vectors during optimization, potentially overlooking their inherent structural properties.
Wei Shen +4 more
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Convergence Analysis of Optimization Algorithms
CoRR, 2017 The regret bound of an optimization algorithms is one of the basic criteria for evaluating the performance of the given algorithm. By inspecting the differences between the regret bounds of traditional algorithms and adaptive one, we provide a guide for choosing an optimizer with respect to the given data set and the loss function.
HyoungSeok Kim +7 more
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Identifying the Unknown Source in Linear Parabolic Equation by a Convoluting Equation Method
Mathematics, 2022 This article is devoted to identifying a space-dependent source term in linear parabolic equations. Such a problem is ill posed, i.e., a small perturbation in the input data may cause a dramatically large error in the solution (if it exists).
Zhenping Li +2 more
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An Analysis of the Convergence of Graph Laplacians [PDF]
, 2011 Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include previously unstudied graphs including kNN graphs.
Daniel Ting +2 more
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Convergence Analysis of Decentralized ASGD
CoRR, 2023 Over the last decades, Stochastic Gradient Descent (SGD) has been intensively studied by the Machine Learning community. Despite its versatility and excellent performance, the optimization of large models via SGD still is a time-consuming task. To reduce training time, it is common to distribute the training process across multiple devices.
Mauro Dalle Lucca Tosi, Martin Theobald
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On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus
Fractal and Fractional, 2021 Quantum calculus (also known as the q-calculus) is a technique that is similar to traditional calculus, but focuses on the concept of deriving q-analogous results without the use of the limits.
Gul Sana +4 more
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