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entropy function-Based Algorithms for Solving a Class of Nonconvex Minimization Problems

Journal of the Operations Research Society of China 2015年第4期3卷 441-458页

作者： Yu-Fan Li Zheng-Hai Huang Min Zhang Department of Mathematics School of ScienceTianjin UniversityTianjin 300072China Center for Applied Mathematics of Tianjin University Tianjin 300072China

Recently,the l_(p)minimization problem(p∈(0,1))for sparse signal recovery has been studied a lot because of its *** this paper,we propose a general smoothing algorithmic framework based on the entropy function for solving a class of l_(p)minimization problems,which includes the well-known unconstrained l_(2)-l_(p)problem as a special *** show that any accumulation point of the sequence generated by the proposed algorithm is a stationary point of the l_(p)minimization problem,and derive a lower bound for the nonzero entries of the stationary point of the smoothing *** implement a specific version of the proposed algorithm which indicates that the entropy function-based algorithm is effective.

关键词： l_(p)minimization problem entropy function Smoothing conjugate gradient method

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entropy function for Multifractal Thermodynamics

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 83-86页

作者： Qiuhua ZENG (Department of Physics, Sichuan University, Chengdu 610064, China) Email: nonlinear@*** Department of Physics Sichuan University Chengdu 610064 China

The theory on multifractal thermodynamics has been studied by the method of series expansion. The method is able to overcome the shortages of Kohmoto’s steepest desent method and the results have general meanings.

关键词： multifractal thermodynamics classical thermodynamics entropy function

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Properties of Fuzzy entropy Based on the Shape Change of Membership function

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Journal of Donghua University(English Edition) 2007年第2期24卷 268-271页

作者：卿铭秦应兵 Department of Mathematics Southwest Jiaotong University

Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, play a significant role in analysis of the change of fuzziness of a fuzzy system because a fuzzy partition consists of a set of fuzzy sets which satisfy some special constraints. This paper has shown several results about entropy changes of a fuzzy set. First, the entropies of two same type of fuzzy sets have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Second, as for Triangular Fuzzy Numbers （TFNs）, the entropies of any two TFNs which can not be always the same type, also, have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Hence, any two TFNs with the same sizes of support intervals have the same entropies. Third, concerning two Triangular Fuzzy Sets （TFSs） with same sizes of support intervals and different heights, the relationship of their entropies lies on their height. Finally, we point it out a mistake that Chen＇s assertion that the entropy of resultant fuzzy set of elevation operation is directly to that of the original one while elevation factor just acts as a propartional factor. These results should contribute to the analysis and design of a fuzzy system.

关键词： fuzzy entropy membership function entropy function triangular fuzzy number support interval

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Maximum-entropy clustering algorithm and its global convergence analysis

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Science China(Technological Sciences) 2001年第1期44卷 89-101页

作者：张志华郑南宁史罡 Institute of Artificial Intelligence & Robotics Xi’ an Jiaotong University Xi’an China

Constructing a batch of differentiable entropy functions touniformly approximate an objective function by means of the maximum-entropy principle, a new clustering algorithm, called maximum-entropy clustering algorithm, is proposed based on optimization theory. This algorithm is a soft generalization of the hard C-means algorithm and possesses global convergence. Its relations with other clustering algorithms are discussed.

关键词： clustering algorithm maximum-entropy principle optimization method entropy function convergence

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