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Convergence problems due to an RBF classifier's learning process

NEURAL PROCESSING LETTERS 1996年第3期3卷 151-162页

作者： Zubiri, E Bour, JC Billat, A FAC SCI LAB APPL MICROELECTF-51687 REIMS 2FRANCE

In this paper, we present the architecture of an RBF neural classifier. We show that a global learning algorithm concentrating only on the centres, the Gaussian widths and the weights of the connections is inadequate for this architecture. Then, we propose to use an hybrid learning algorithm in which the Gaussian centres are first fixed. This one gives satisfactory results.

关键词： classification convergence gradient algorithm RBF

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Formulating and solving a class of optimization problems for high-performance gray world automatic white balance

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APPLIED SOFT COMPUTING 2011年第1期11卷 523-533页

作者： Chen, Cheng-Lun Lin, Shao-Hua Natl Chung Hsing Univ Dept Elect Engn Taichung 40227 Taiwan

This paper provides new insights into methods performing automatic white balance for a digitally captured image. It is shown that automatic white balance may be formulated as an optimization problem with explicit definition of objective function, decision variables, and constraints. Three alternative methods of formulating the optimization problem are proposed. It is also shown that fuzzy inference rules, commonly utilized in existing literatures to evaluate to what degree an image satisfying the gray world assumption, may be incorporated into the objective function of the optimization problem. A two-stage adjustment law with constrained search direction is then proposed to update the decision variables. A gradient descent algorithm is employed to numerically solve the problem, which guarantees the convergence and that optimal white balance effort is achieved for most images. Experimental results and a comparative study justify that the proposed methods are preferable to existing methods with regard to the execution time, the algorithmic complexity, and the performance. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Color balance Fuzzy system gradient algorithm Gray world assumption White balance

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A Reflected Inertial Krasnoselskii-Type algorithm for Lipschitz Pseudo-Contractive Mappings

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BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY 2018年第4期44卷 1109-1115页

作者： Moudafi, A. Aix Marseille Univ Fac Sci St Jerome CNRS Lab Informat & SystUMR 7296 F-13397 Marseille France

It is well-known that Mann's algorithm fails to converge for Lipschitz pseudo-contractive mappings and strong convergence of Ishikawa's algorithm for Lipschitz pseudo-contractive mappings T have not been achieved without compactness assumption on T or on the underlying closed convex set C. In this note, we develop a convergence result of, xn+ 1 = PC x(n)-1 + (1 -2.) xn +.T (2xn -xn-1) a Reflected Inertial Krasnoselskii-type algorithm for finding fixed-points of Lipschitz pseudo-contractive mappings in Hilbert spaces with an application to a split feasibility/fixed-point problem.

关键词： Lipschitz pseudo-contractive mappings gradient algorithm Ishikawa process Reflection

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Approximate solution of the p-median minimization problem

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2016年第9期56卷 1591-1597页

作者： Il'ev, V. P. Il'eva, S. D. Navrotskaya, A. A. Russian Acad Sci Siberian Branch Inst Math Pr Akad Koptyuga 4 Novosibirsk 630090 Russia Omsk State Univ Pr Mira 55A Omsk 644077 Russia

A version of the facility location problem (the well-known p-median minimization problem) and its generalization-the problem of minimizing a supermodular set function-is studied. These problems are NP-hard, and they are approximately solved by a gradient algorithm that is a discrete analog of the steepest descent algorithm. A priori bounds on the worst-case behavior of the gradient algorithm for the problems under consideration are obtained. As a consequence, a bound on the performance guarantee of the gradient algorithm for the p-median minimization problem in terms of the production and transportation cost matrix is obtained.

关键词： combinatorial optimization p-median supermodular set function gradient algorithm performance guarantee

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Tracking Analysis of Complex Adaptive IIR Notch Filter for a Linear Chirp Signal

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2009年第6期E92A卷 1526-1529页

作者： Mvuma, Aloys Nishimura, Shotaro Hinamoto, Takao Univ Dodoma Sch Informat Dodoma Tanzania Shimane Univ Matsue Shimane 6908504 Japan Hiroshima Univ Grad Sch Higashihiroshima 7398527 Japan

This paper analyzes frequency tracking characteristics of a complex-coefficient adaptive infinite impulse response (IIR) notch filter with a simplified gradient-based algorithm. The input signal to the complex notch filter is a complex linear chirp embedded in a complex zero-mean white Gaussian noise. The analysis starts with derivation of a first-order real-coefficient difference equation with respect to steady-state instantaneous frequency tracking error. Closed-form expression for frequency tracking mean square error (MSE) is then derived from the difference equation. Lastly, closed-form expressions for optimum notch bandwidth coefficient and step size constant that minimize the frequency tracking MSE are derived. Computer simulations are presented to validate the analysis.

关键词： adaptive notch filter gradient algorithm linear chirp signal tracking MSE

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Optimized Distributed MIMO for Cooperative Relay Networks

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IEEE COMMUNICATIONS LETTERS 2010年第1期14卷 9-11页

作者： He, Xin Luo, Tao Yue, Guangxin Beijing Univ Posts & Telecommun Dept Informat & Commun Engn Beijing 100876 Peoples R China

This paper presents an optimized distributed multiple-input multiple-output (OD-MIMO) for cooperative communication in wireless relay networks. The set of cooperating nodes is a priori unknown. In order to avoid the centralized stream and pilot allocation procedure, a fixed signature vector (SV) is assigned for each node in the network. We analyze the constraints of the proposed scheme, and derive an optimization criterion for the decision of the SVs. A gradient-based algorithm for SV design is provided. Simulation results show that the performance loss of OD-MIMO compared to centralized distributed MIMO is small for large number of cooperative relay nodes.

关键词： Distributed MIMO gradient algorithm cooperative relay

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Online learning under one sided σ-smooth function

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2024年第5期47卷 76-76页

作者： Zhang, Hongxiang Xu, Dachuan Gai, Ling Zhang, Zhenning Univ Chinese Acad Sci Sch Math Sci Beijing 100049 Peoples R China Beijing Univ Technol Inst Operat Res & Informat Engn Beijing 100124 Peoples R China Univ Shanghai Sci & Technol Business Sch Sch Intelligent Emergency Management Shanghai 200093 Peoples R China

The online optimization model was first introduced in the research of machine learning problems (Zinkevich, Proceedings of ICML, 928-936, 2003). It is a powerful framework that combines the principles of optimization with the challenges of online decision-making. The present research mainly consider the case that the reveal objective functions are convex or submodular. In this paper, we focus on the online maximization problem under a special objective function Phi(x) : [0,1](n) -> R+ which satisfies the inequality 1/2 < u(T) del(2)Phi(x), u > <= sigma center dot ||u||(1)/||x||(1) < u, del Phi(x)> for any x, u is an element of[0, 1](n), x not equal 0. This objective function is named as one sided sigma-smooth (OSS) function. We achieve two conclusions here. Firstly, under the assumption that the gradient function of OSS function is L-smooth, we propose an (1-exp((theta - 1)(theta/(1+theta))(2 sigma)))- approximation algorithm with O(root T) regret upper bound, where T is the number of rounds in the online algorithm and theta, sigma is an element of R+ are parameters. Secondly, if the gradient function of OSS function has no L-smoothness, we provide an (1 + ((theta + 1)/theta)(4 sigma))(-1)-approximation projected gradient algorithm, and prove that the regret upper bound of the algorithm is O(root T). We think that this research can provide different ideas for online non-convex and non-submodular learning.

关键词： Online optimization L-smooth gradient algorithm

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New algorithm for extreme temperature measurements

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ADVANCES IN ENGINEERING SOFTWARE 2000年第4期31卷 275-285页

作者： Damean, N Univ Twente NL-7500 AE Enschede Netherlands

A new algorithm for measurement of extreme temperature is presented. This algorithm reduces the measurement of the unknown temperature to the solving of an optimal control problem, using a numerical computer. Based on this method, a new device for extreme temperature measurements is projected. It consists of a hardware part that includes some standard temperature sensors and it also has a software section. The principal component of the device is a rod. The Variation in the temperature, which is produced near one end of the rod, is determined using some temperature measurements at the other end of the rod and the new algorithm described here. The mathematical model of the device and the algorithm are explained in detail. At the same time, some possible practical implementations and a collection of simulations are presented. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： gradient algorithm local variation method numerical method heat equation temperature measurement

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On geometric algorithms for real-time grasping force optimization

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 2004年第6期12卷 843-859页

作者： Liu, GF Xu, JJ Li, ZX Hong Kong Univ Sci & Technol Dept Elect & Elect Engn Kowloon Hong Kong Peoples R China

Grasping force optimization with nonlinear friction constraints is a fundamental problem in dextrous manipulation with multifingered robotic hands., Over the last few years, by transforming the problem into convex optimization problems on Riemannian manifolds of, symmetric and positive definite matrices, significant advances have been achieved in this area. Five promising algorithms: two gradient algorithms, two Newton algorithms, and one interior point algorithm have been proposed for real-time solutions of the problem. In this paper, we present in a unified geometric framework, the derivation of these five algorithms and the selection of step sizes for each algorithm. Using the geometric structure of the affine-scaling vector fields associated with the optimization problem, we prove that some of these algorithms have quadratic convergence properties, and their continuous versions are exponentially convergent. We evaluate the performance of these algorithms through simulation and experimental studies with the Hong Kong University of Science and Technology (HKUST) three-fingered hand. This study will facilitate selection and implementation of grasping force optimization algorithms for similar applications.

关键词： affine-scaling vector fields convergence analysis gradient algorithm interior point algorithm Newton algorithm semidefinite programming step size selection

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An observer-based state feedback control of parametrically excited systems

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SYSTEMS & CONTROL LETTERS 1997年第2-3期30卷 119-125页

作者： Chen, MS Fu, RJ Department of Mechanical Engineering National Taiwan University No. 1 Roosevelt Rd. Sec. 4 Taipei 106 Taiwan ROC

In the study of adaptive parameter identification, the parameter error dynamics resulting from the gradient algorithm represents a very special class of parametrically excited system, whose stability condition has been studied thoroughly. By utilizing this stability condition, one can develop a new active control design for a parametrically excited system which exhibits sustained but bounded oscillations due to the time-varying system matrix. The resultant observer-based state feedback control guarantees exponential decay of the state oscillation given that the system is both uniformly controllable and uniformly observable. The advantage of the proposed design is that it requires neither information of time derivatives of the parametric excitations, nor predicting future information of the parametric excitations. (C) 1997 Elsevier Science B.V.

关键词： linear time-varying system parametric excitation gradient algorithm state feedback control observer

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