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Analysis and Synthesis of gradient algorithms Based on Fractional-Order System Theory

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2023年第3期53卷 1895-1906页

作者： Wei, Yiheng Chen, Yuquan Zhao, Xuan Cao, Jinde Southeast Univ Sch Math Nanjing 211189 Peoples R China Hohai Univ Coll Energy & Elect Engn Nanjing 211106 Peoples R China Yonsei Univ Yonsei Frontier Lab Seoul 03722 South Korea

In this study, a framework for processing gradient algorithms is proposed in accordance with nabla fractional-order system theory. Unlike most of the literature, the gradient algorithm is initially recast into a nabla fractional-order dynamic system. To be specific, the algorithm is designed using control theory and analyzed using the Lyapunov theory, which is a more general and effective way to render high-performance algorithm. Three types of algorithms are built in this study, i.e., the asymptotic convergence case, the finite-time convergence case, and the fixed-time convergence case. Finally, a comprehensive simulation study is conducted verifying the correctness, usefulness, and practicality of the framework.

关键词： Convergence Optimization Machine learning algorithms Heuristic algorithms Linear programming Fractional calculus Stability criteria Convex optimization discrete fractional calculus finite-time convergence fixed-time convergence gradient algorithm Lyapunov method

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CONVERGENCE ANALYSIS OF gradient algorithmS ON RIEMANNIAN MANIFOLDS WITHOUT CURVATURE CONSTRAINTS AND APPLICATION TO RIEMANNIAN MASS

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SIAM JOURNAL ON OPTIMIZATION 2021年第1期31卷 172-199页

作者： Wang, Jinhua Wang, Xiangmei Li, Chong Yao, Jen-Chih Hangzhou Normal Univ Dept Math Hangzhou 311121 Peoples R China Guizhou Univ Coll Math & Stat Guiyang 550025 Guizhou Peoples R China Zhejiang Univ Sch Math Sci Hangzhou 310027 Zhejiang Peoples R China China Med Univ Ctr Gen Educ Taichung Taiwan Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 40402 Taiwan

We study the convergence issue for the gradient algorithm (employing general step sizes) for optimization problems on general Riemannian manifolds (without curvature constraints). Under the assumption of the local convexity/quasi-convexity (resp., weak sharp minima), local/global convergence (resp., linear convergence) results are established. As an application, the linear convergence properties of the gradient algorithm employing the constant step sizes and the Armijo step sizes for finding the Riemannian L-p (p is an element of [1,+infinity)) centers of mass are explored, respectively, which in particular extend and/or improve the corresponding results in [B. Afsari, R. Tron, and R. Vidal, SIAM J. Control Optim., 51 (2013), pp. 2230--2260;G. C. Bento et al., J. Optim. Theory Appl., 183 (2019), pp. 977--992].

关键词： Riemannian manifold sectional curvature gradient algorithm local convergence global convergence linear convergence Riemannian center of mass

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Comparison of a gradient-Based and LASSO (ISTA) algorithm for Sparse Signal Reconstruction 5

Comparison of a Gradient-Based and LASSO (ISTA) Algorithm fo...

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5th Mediterranean Conference on Embedded Computing (MECO)

作者： Vujovic, Stefan Stankovic, Isidora Dakovic, Milos Stankovic, Ljubisa Univ Montenegro Podgorica Montenegro

ISBN: (纸本)9781509022212

Sparse signal reconstruction performed by two different algorithms is considered. First algorithm is the ISTA algorithm for LASSO minimization, while the second one is the gradient-based descent algorithm. algorithms perform signal reconstruction in a completely different way. The ISTA algorithm reconstructs signals in the sparsity transformation domain. The gradient descent algorithm performs reconstruction in time/measurements domain, considering the missing samples as variables. Both of them use the l(1)-norm in minimization. Computational time and mean absolute error are used in comparison analysis presented in this paper.

关键词： Compressive sensing gradient algorithm Sparse reconstruction Sparse signals Lasso minimization Ista algorithm

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An upper bound of the step size for the gradient Constant Modulus algorithm

An upper bound of the step size for the gradient Constant Mo...

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Conference on Photonics, Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments IV

作者： Dziwoki, G Silesian Tech Univ Inst Elect PL-44100 Gliwice Poland

The paper presents the theoretical derivation of an upper bound of the step size for the CM blind equalization algorithm. The analysis is performed under following assumptions, among other things: SISO (Single Input S... 详细信息

ISBN: (纸本)081946211X

关键词： CM algorithm gradient algorithm step size whitening filtering

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Analysis and Application of gradient Adaptive Lattice Filtering algorithm

Analysis and Application of Gradient Adaptive Lattice Filter...

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International Conference on Computer and Electrical Engineering

作者： Qi, Haibing Huangshi Inst Technol Sch Elect & Elect Informat Eng Huangshi Peoples R China

ISBN: (纸本)9780769535043

Benefiting from self-orthogonal backward output signal and other excellent numerical characters, the lattice filters offer many promising advantages over transversal filters for realization on modern digital processor, but how long and how much reflectance coefficients are difficult to be selected in engineering application as the veiled transfer functions of the structure. Introducing gradient algorithm in each lattice section, we advanced a new project which the optimal parameters of sections and step could be acquired through the outcome of the astringency and stability of reflectance in simulation. In the meantime through constituting a joint processing filter with the lattice filter and LMS filter, we had verified the method reasonably and effectively. The result shows that the project can ensure to contrive lattice filter in the hardware aspect conveniently, and it need less hardware resources comparing with original algorithm.

关键词： lattice structure gradient algorithm reflection coefficient adaptive filter

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A gradient BYY Harmony Learning algorithm for Straight Line Detection

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5th International Symposium on Neural Networks

作者： Chen, Gang Li, Lei Ma, Jinwen Peking Univ Sch Math Sci Dept Informat Sci Beijing 100871 Peoples R China

ISBN: (纸本)9783540877318

Straight line detection is a basic problem in image processing and has been extensively studied from different aspects, but most of the existing algorithms need to know the number of straight lines in an image in advance. However, the Bayesian Ying-Yang (BYY) harmony learning can make model selection automatically during parameter learning for the Gaussian mixture modeling, which can be further applied to detecting the correct number of straight lines automatically by representing the straight lines with Gaussians or Gaussian functions. In this paper, a, gradient BYY harmony learning algorithm is proposed to detect the straight lines automatically from an image as long as the pre-assumed number of straight lines is larger than the true one. It is demonstrated by the simulation and real image experiments that this gradient BYY harmony learning algorithm can not, only determine the number of straight lines automatically, but also detect the straight lines accurately, against noise.

关键词： Bayesian Ying-Yang (BYY) harmony learning gradient algorithm Automated model selection Straight line detection

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Theoretical Performance of the gradient-Based Tone Reservation PAPR Reduction algorithm 16

Theoretical Performance of the Gradient-Based Tone Reservati...

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16th International Conference on Wireless and Mobile Computing, Networking and Communications (IEEE WiMob)

作者： El Hassan, Mariam Crussiere, Matthieu Helard, Jean-Francois Nasser, Youssef Bazzi, Oussama Univ Rennes CNRS INSA Rennes IETR UMR6164 F-35000 Rennes France Lebanese Univ Fac Sci Hadath Rafic Hariri Univ Campus Hadath Lebanon Amer Univ Beirut Beirut 11072020 Lebanon

ISBN: (纸本)9781728197227

In this paper, we provide a theoretical analysis on the performance of the famous gradient-based Tone-Reservation PAPR reduction algorithm. To that end, we study the amplitude statistical distribution of the time domain OFDM signals to which PAPR reduction has been applied. Such distribution is then integrated into a generic EVM expression in order to provide a closed form expression of this latter, which is validated and analyzed through numerical simulations. Thanks to this work, we provide theoretical tools to analytically assess the performance of the gradient method relatively to the optimal TR algorithm, and hence allow further analysis about the complexity-PAPR reduction efficiency trade-off of TR PAPR reduction algorithms, which could be useful for the optimization of the power efficiency of any multicarrier system.

关键词： Analytical expression EVM OFDM PAPR reduction Probability distribution Tone Reservation gradient algorithm

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gradient fault detecting algorithm for pitch system of wind turbine using the filtering technique 36

Gradient fault detecting algorithm for pitch system of wind ...

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第36届中国控制会议

作者： Ziyun Wang Zhicheng Ji Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education) Jiangnan University

ISBN: (纸本)9781538629185

A fault detection problem of pitch system in wind turbine is considered in this ***,a second-order model is formulated to illustrate the hydraulic pitch of wind turbine and a bilinear transformation method is used to derive the identification model of pitch ***,the fault detection problem is transformed into the parameter estimation issue and a gradient filtering estimation algorithm is ***,the example shows the effectiveness and practicability of the presented fault detecting algorithm.

关键词： gradient algorithm System identification Fault detection Filtering technique Pitch system modeling

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Blind Source Separation for OFDM with gradient algorithms

Blind Source Separation for OFDM with Gradient Algorithms

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6th International Conference on Computer Sciences and Convergence Information Technology (ICCIT)

作者： Sriyananda, M. G. S. Joutsensalo, J. Hamalainen, T. Univ Jyvaskyla Dept Math Informat Technol Fac Informat Technol FI-40014 Jyvaskyla Finland

ISBN: (纸本)9788988678558

Signal recovery mechanism for Orthogonal Frequency Division Multiplexing (OFDM) with the assistance of principles of Blind Source Separation (BSS) and gradient algorithm (GA) is presented. Elimination or reduction of undesirable influences encountered with in the wireless interface is targeted by using a set of filter coefficients. Four scalar energy functions are used in deriving the filter coefficients. Energy criterion functions to be optimized and the performance is justified. Time correlation properties of the channel are used as advantages in introducing the energy functions. Performance of the algorithms is evaluated when they are used for a synchronous downlink OFDM model. Simulations are carried out under slow fading channel conditions with a receiver containing Equal Gain Combining (EGC) and BSS algorithms. It could be noted that, better performance for this predominant multicarrier air interface communication technique can be achieved with this combined scheme. It is important grasp the fact that, these schemes can be promoted as low complexity simple matrices based processing mechanisms.

关键词： Blind Source Separation gradient algorithm OFDM Slow Fading

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Numerical shape reconstruction approaches for solving free boundary inverse problem for the p-Laplacian operator

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2025年 463卷

作者： Chakib, Abdelkrim Khalil, Ibrahim Sultan Moulay Slimane Univ Fac Sci & Tech Appl Math Team AMT Beni Mellal Morocco

In this paper, we develop efficient numerical shape reconstruction approaches for solving the Bernoulli free boundary inverse problem, constrained by a nonlinear elliptic problem for the p-Laplacian operator. In this framework, let us first mention that, to our best knowledge, the numerical resolution of this problem has never been investigated in previous works, for different values of p > 1. So, we propose here a shape optimal design formulation of this inverse free boundary problem and address its shape sensitivity analysis using both distributed and boundary types of Eulerian derivatives. Then, we develop two numerical gradient shape optimization processes for solving this shape optimization problem, based on the distributed and the boundary shape derivative formulas, performed with the Picard iterations procedure and the finite element Galerkin discretization, for solving the auxiliary nonlinear boundary value problem involving p-Laplacian operator. Finally, several numerical results are presented in two and three dimensions, showing that the shape optimization gradient process based on the distributed Eulerian derivative is more efficient than the one based on the classical boundary shape derivative, in solving this kind of problems.

关键词： Shape optimization Bernoulli problem p-Laplacian operator Shape derivative Distributed formula Boundary formula gradient algorithm Finite elements approximation

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