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57th ELMAR International Symposium

作者： Vujovic, Stefan Orovic, Irena Dakovic, Milos Stankovic, Ljubisa Univ Montenegro Fac Elect Engn Podgorica Montenegro

ISBN: (纸本)9789531842099

The paper presents a statistical performance analyzer for compressive sensing gradient algorithm. It is composed of two main parts. The first part is designed as a tool for signal reconstruction based on the gradient algorithm. The possibility to generate various signals is incorporated through the special panel which is used to set the length, sparsity, percent of available samples and the ranges of amplitude. Also, a noise with specified variance can be added through this panel as well. The second part of presented instrument is dedicated to the statistical analysis. Different analysis can be performed through this part such as the calculation of MSE as a function of noise variance or signal sparsity, as well as the analysis of MSE and computational time in terms of sparsity and the amount of missing samples. This instrument can be useful for both the research and educational purpose for the area of compressive sensing and signal reconstruction.

关键词： Statistical Analyzer gradient algorithm Com-pressive Sensing Sparse Signal Processing

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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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gradient APPROXIMATION algorithmS FOR THE σ-OSS plus CONCAVE FUNCTION MAXIMIZATION

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS

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JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS 2025年第1期9卷 15-30页

作者： Zhang, Hongxiang Yang, Wenguo Du, Ding-zhu Univ Chinese Acad Sci Sch Math Sci Beijing 100049 Peoples R China Univ Texas Dallas Dept Comp Sci Dallas TX 75083 USA

This paper studies the one-sided sigma-smooth + concave function maximization problems under general convex sets. Provided that the objective function is Lipschitz smooth, we use the jump-start initial point selection technique and the Frank-Wolfe method to propose a [1 - e-(1-alpha)eta-1], [1 - e-(1-alpha)eta-1] approximation algorithm with O(epsilon-1(n + T)) time complexity, where eta = ( alpha+1)2 sigma, alpha E (0,1), and sigma is a finite constant. The algorithm is discrete-time and receives O losses. To overcome the disadvantage that the gradient of function is Lipschitz continuous, we propose the continuous-time JumpStart Greedy Frank-Wolfe algorithm with the same approximation guarantee. In addition, through the analysis of our algorithms, we investigate some important theoretical properties regarding the analysis of approximation algorithms for continuous function maximization problems.

关键词： . Approximation algorithm Continuous function maximization problem Frank-Wolfe method gradient algorithm OSS plus concave

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Steady-state analysis of a complex adaptive notch filter using modified gradient algorithm

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AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS 2014年第11期68卷 1112-1118页

作者： Punchalard, R. Mahanakorn Univ Technol Dept Telecommun Engn Bangkok 10530 Thailand

Based on power spectral density (PSD) analytical technique, mean square error (MSE) (or variance) of the frequency estimate of a first-order complex adaptive IIR notch filter (ANF) using modified complex plain gradient (MCPG) algorithm is investigated in this paper. The steady-state expression for MSE is derived in closed form. A quantitative analysis for the estimation MSE has been carried out. It has been revealed that the MSE of frequency estimate is independent of an input frequency of a complex sinusoid. In addition, computer simulations are treated to corroborate the theoretical analysis and the relationships between MSE and system parameters are shown. (C) 2014 Elsevier GmbH. All rights reserved.

关键词： Complex notch filter gradient algorithm Frequency estimation Power spectral density

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A multi-innovation generalized extended stochastic gradient algorithm for output nonlinear autoregressive moving average systems

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APPLIED MATHEMATICS AND COMPUTATION 2014年 247卷 218-224页

作者： Hu, Yuanbiao Liu, Baolin Zhou, Qin China Univ Geosci Minist Land & Resources Key Lab Deep GeoDrilling Technol Beijing 100083 Peoples R China

This paper proposes a generalized extended stochastic gradient (GESG) algorithm for estimating the parameters of a class of Wiener nonlinear autoregressive moving average systems using the gradient search. In order to improve the convergence rates of the GESG algorithm, a multi-innovation GESG algorithm is derived. The simulation results indicate that the proposed algorithms can effectively estimate the parameters of a class of output nonlinear systems. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Parameter estimation Recursive identification gradient algorithm Nonlinear system

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Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm

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JOURNAL OF COMPUTATIONAL NEUROSCIENCE 2014年第3期37卷 569-582页

作者： Chang, Joshua Paydarfar, David Univ Massachusetts Sch Med Dept Neurol Worcester MA 01610 USA Harvard Univ Wyss Inst Biologically Inspired Engn Boston MA 02115 USA

Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli;however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: 1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions;and 2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.

关键词： Computational model gradient algorithm Optimal stimulation Single-cell neuron

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Robust adaptive control for nonlinear discrete-time systems based on DE-GMAW

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CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS 2025年 256卷

作者： Wang, Jing Tian, Engang Yan, Huaicheng Qu, Fanrong Univ Shanghai Sci & Technol Sch Opt Elect & Comp Engn Shanghai 200093 Peoples R China East China Univ Sci & Technol Informat Sci & Engn Shanghai 200093 Peoples R China Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Wuhan Peoples R China

Gas Metal Arc Welding (GMAW) is a critical process in manufacturing, known for its efficiency and versatility. The double-electrode GMAW (DE-GMAW) technique further enhances these attributes, offering superior welding speed and improved melting effects. However, controlling the DE-GMAW process effectively remains a complex challenge due to the nonlinear and dynamic nature of the system. The process involves intricate interactions between electrical, thermal, and mechanical phenomena, resulting in highly nonlinear behavior. Variations in material properties, environmental conditions, and external disturbances can adversely affect the welding process. Moreover, traditional control methods often fail to account for unmodeled dynamics and modeling errors, leading to performance degradation and potential instability. To address these challenges, this paper introduces a robust adaptive control scheme tailored for DE-GMAW systems, which combines online projection estimation identification and pole placement strategy at the same time to compensate for parameter uncertainties, external disturbances, and unmodeled dynamics. Simulation examples in welding process are carried out to demonstrate the effectiveness of the proposed robust adaptive control scheme.

关键词： Robust adaptive control scheme Nonlinear system gradient algorithm Pole assignment self-tuning Double-electrode gas metal arc welding (DE-GMAW)

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A numerical study of vortex nucleation in 2D rotating Bose-Einstein condensates

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MATHEMATICS AND COMPUTERS IN SIMULATION 2025年 229卷 409-434页

作者： Dujardin, Guillaume Lacroix-Violet, Ingrid Nahas, Anthony Univ Lille Inria CNRS UMR 8524 Lab Paul Painleve F-59000 Lille France Univ Lorraine CNRS IECL F-54000 Nancy France Univ Lille CNRS UMR 8524 InriaLab Paul Painleve F-59000 Lille France

This article implements a numerical method for the minimization under constraints of a discrete energy modelling multicomponents rotating Bose-Einstein condensates in the regime of strong confinement and with rotation. Moreover, this method allows to consider both segregation and coexistence regimes between the components. The method includes a discretization of a continuous energy in space dimension 2 and a gradient algorithm with adaptive time step and projection for the minimization. It is well known that, depending on the regime, the minimizers may display different structures, sometimes with vorticity (from singly quantized vortices, to vortex sheets and giant holes). The goal of this paper is to study numerically the structures of the minimizers. In order to do so, we introduce a numerical algorithm for the computation of the indices of the vortices, as well as an algorithm for the computation of the indices of vortex sheets. Several computations are carried out, to illustrate the efficiency of the method, to cover different physical cases, to validate recent theoretical results as well as to support conjectures. Moreover, we compare this method with an alternative method from the literature.

关键词： Bose-Einstein condensation Gross-Pitaevskii energy Segregation and coexistence regimes Minimization under constraints gradient algorithm Vortex detection Vortex quantization Numerical experiments

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On a numerical approach for solving some geometrical shape optimization problems in fluid mechanics

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2024年 128卷

作者： Chakib, Abdelkrim Khalil, Ibrahim Ouaissa, Hamid Sadik, Azeddine Sultan Moulay Slimane Univ Fac Sci & Tech Appl Math Team AMT Beni Mellal Morocco Abdelmalek Essaadi Univ Normal Higher Sch Appl Math & Comp Sci Team AMCST Tetouan Morocco

This paper is devoted to the numerical study of geometrical shape optimization problems in fluid mechanics, which consist in minimizing some criterion volume cost functionals on a family of admissible doubly connected domains, constrained by steady-state Stokes boundary value problems. We establish the existence of the shape derivative of the considered cost functionals, by means of Minkowski deformation, using the shape derivative formulas, recently established in Boulkhemair and Chakib (2014). This allows us to express the shape derivative by means of the support function and to avoid the tedious computations required when one use the gradient optimization process based on the classical shape derivative, involving the vector fields, notably when one opt for the finite element discretization. So, based on the established shape derivative formulas, we propose a shape optimization numerical process for solving these problems, using the gradient descent algorithm performed by the finite element discretization, for approximating the auxiliary boundary value Stokes problems. Finally, in order to show the validity and the effectiveness of the proposed approach, we present some numerical tests obtained by solving some shape optimization problems of minimizing different cost functionals on various configurations of domains, constrained by steady-state stokes boundary value problems with different boundary conditions. These numerical simulations include some comparison results showing that the proposed approach is more efficient than the gradient approach based on the classical shape derivative, in terms of the accuracy of the solution and central processing unit (CPU) time execution.

关键词： Shape optimization Fluid mechanics Stokes equation Shape derivative Doubly connected domains Minkowski deformation Convex domains Support functions gradient algorithm Finite elements approximation

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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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