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Bi-extrapolated subgradient projection algorithm for solving multiple-sets split feasibility problem

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Applied Mathematics(A Journal of Chinese Universities) 2014年第3期29卷 283-294页

作者： DANG Ya-zheng GAO Yan College of Computer Science and Technology (Software College) Henan Polytechnic University School of Management University of Shanghai for Science and Technology

This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.

关键词： Multiple-sets split feasibility problem subgradient accelerated iterative algorithm convergence.

An Extrapolated Parallel subgradient Projection Algorithm with Centering Technique for the Convex Feasibility Problem

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Chinese Quarterly Journal of Mathematics 2014年第1期29卷 22-29页

作者： DANG Ya-zheng HAN Xue-feng GAO Yan School of Management University of Shanghai for Science and Technology Shanghai 200093 China College of Compiler Science and Technology Henan Polytechnic University Jiaozho 454000 China

In this paper,we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem,the algorithm improves the convergence by reason of using centering techniques which reduce the oscillation of the corresponding sequence.To prove the convergence in a simply way,we transmit the parallel algorithm in the original space to a sequential one in a newly constructed product space.Thus,the convergence of the parallel algorithm is derived with the help of the sequential one under some suitable conditions.Numerical results show that the new algorithm has better convergence than the existing algorithms.

关键词： convex feasibility problem subgradient centering technique product space convergence

NONDESCENT subgradient METHOD FOR NONSMOOTH CONSTRAINED MINIMIZATION

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Numerical Mathematics A Journal of Chinese Universities(English Series) 1994年第2期3卷 126-134页

作者：徐慧福 Department of Mathematics Ningbo University Ningbo 315211 Zhejiang Province PRC.

A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general global minimiizing algorithm is employed as a subroutine of the algorithm. The method is expected to tackle a large class of nonsmooth constrained minimization problem.

关键词： Nonsmooth constrained minimization duality subgradient method stopping rule convergence.

An effective framework for characterizing rare categories

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Frontiers of Computer Science 2012年第2期6卷 154-165页

作者： JingruiHE，HanghangTONG，JaimeCARBONELL。 HanghangTONG SJaimeCARBONELL IBMT．J．WatsonResearchCenter YorktownHeightsNY10598USA SchoolofComputerScience CarnegieMellonUniversityPittsburghPA15213USA

Rare categories become more and more abundant and their characterization has received little attention thus far. Fraudulent banking transactions, network intrusions, and rare diseases are examples of rare classes whose detection and characterization are of high value. However, accurate char- acterization is challenging due to high-skewness and non- separability from majority classes, e.g., fraudulent transac- tions masquerade as legitimate ones. This paper proposes the RACH algorithm by exploring the compactness property of the rare categories. This algorithm is semi-supervised in na- ture since it uses both labeled and unlabeled data. It is based on an optimization framework which encloses the rare exam- ples by a minimum-radius hyperball. The framework is then converted into a convex optimization problem, which is in turn effectively solved in its dual form by the projected sub- gradient method. RACH can be naturally kernelized. Experi- mental results validate the effectiveness of RACH.

关键词： rare category minority class characterization,compactness optimization hyperball subgradient

Nonsmooth identification of mechanical systems with backlash-like hysteresis

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控制理论与应用（英文版） 2013年第3期11卷 477-482页

作者： Ruili DONG Yonghong TAN David HE College of Mechanical and Electronic Technology Shanghai Normal University Department of Mechanical and Industrial Engineering University of Illinois

Backlash-like hysteresis is one of the nonsmooth and multi-valued nonlinearities usually existing in mechanical systems. The traditional identification method is quite difficult to be used to model the systems involved with such complex nonlinearities. In this paper, a nonsmooth recursive identification algorithm for the systems with backlash-like hysteresis is proposed. In this method, the concept of Clarke subgradient is introduced to approximate the gradients at nonsmooth points and the so-called bundle method is used to obtain the optimization search direction in nonsmooth cases. Then, a recursive algorithm based on the idea of bundle method is developed for parameter estimation. After that, the convergence analysis of the algorithm is investigated. Finally, simulation results to validate the proposed method on a simulated mechanical transmission system are presented.

关键词： Identification Mechanical system Pseudo-Hammerstein model Backlash Bundle method subgradient

Distributed algorithms for solving the convex feasibility problems

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Science China(Information Sciences) 2020年第8期63卷 242-244页

作者： Kaihong LU Gangshan JING Long WANG Center for Complex Systems School of Mechano-electronic EngineeringXidian University Department of Applied Mathematics Hong Kong Polytechnic University Center for Systems and Control College of EngineeringPeking University

Dear editor,Along with the recent adoption of multi-agent networks [1–9], consensus-based distributed optimization has been extensively investigated. In [1], a distributed algorithm that combines the consensus and subgradient algorithms was developed for obtaining the solution of the unconstrained convex distributed optimization problems. In [2], a distributed discrete-time projected subgradient al-

关键词： Multi-agent systems Consensus Convex inequalities subgradient Projection

The Uniqueness of Market Economy in China

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Systems Science and Systems Engineering 1995年第2期5卷 179-192页

作者： DENC Shuhui JIN Xing CHEN Bin(Institute of Systems Science, Academia Sinica,Beijing 100080, P.R.China)

The purpose of this paper is to prove the equilibrium of general equilibrium of market economy in China. As a consequence,it is shown that, when the governmentplanning system gradually loses its function,the corresponding equilibrium point sequence of planned/market mixed economy converges to the unique equilibrium point of market economy. This demonstrates that the transition of China’s planned/market mixed economy to market economy will be stable.

关键词： planned/market mixed economy market economy government plan system uniqueness of equilibrium solution subgradient essentially smooth.

THE　OPTIMUM　SELECTION　FOR　A　CONTINUOUS　TYPE　EUCLIDEAN　MULTIFACILITY　LOCATION

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Systems Science and Mathematical Sciences 1996年第2期9卷 101-106页

作者： GAO Chengyun (Institute of Automation, Qufu Normal University, Qufu 273165, China) 曲阜师范大学自动化所山东曲阜 273165

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关键词： Continuous type multifacility location subgradient algorithm convergence

THE RELATIONSHIP BETWEEN THE CONE-WEAK SUBDIFFERENTIAL AND CONE-WEAK DIRECTION DERIVATIVE FOR CONVEX SET-VALUED MAPPING

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Systems Science and Mathematical Sciences 2000年第3期13卷 327-332页

作者： $MENG Zhiqing(Department of Computer Science, Xiangtan University, Hunan 411105 Department of Applied Mathematics Xidian University, Xi,an 710071, China)HU Yuda(Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai 200030, China) 湘潭大学计算机系湖南长沙 411105 上海交通大学应用数学系上海 200030

In this paper, we introduce the concepts of the conesweak subdifferential and the cone-weak direction derivative of convex set-valued mapping in a locally convex topological vector space. We study the relationship bet... 详细信息

关键词： Set-valued mapping cone-weak subgradient cone-weak subdifferential coneweak direction derivative