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One-step quadratic convergence.of noninterior continuation method for NCP

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Chinese Science Bulletin 1999年第20期44卷 1858-1862页

作者： XIU NaihuaDepartment of Mathematics , Northern Jiaotong University , Beijing 100044, China Department of Mathematics Northern Jiaotong University Beijing China

A noninterior continuation method is presented, with only the certering step used at each iteration, for nonlinear complementarity problem. It is shown that the algorithm is globally linearly and locally quadratically... 详细信息

关键词： nonlinear complementarity problem noninterior continuation method one-step quadratic convergence.

FEASIBLE POINT METHODS AND THEIR GLOBAL convergence

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Chinese Science Bulletin 1992年第8期37卷 617-622页

作者：胡晓东韩继业 Institute of Applied Mathematics Academia Sinica Beijing 100080 PRC

Ⅰ. INTRODUCTIONIt is efficient and simple to study and design, by some unified approaches, the structures of algorithms in nonlinear programming, e.g. Huang succeeded in treating the quasi-Newton methods in terms of the variation of several parameters; Zangwill introduced the point-to-set mappings with which he discussed the convergence.properties of

关键词： constrained optimization feasible point methods global convergence.

ON convergence.OF TAIL PROBABILITY SERIES IN LAW OF LARGE NUMBERS

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Science China Mathematics 1989年第12期32卷 1423-1436页

作者：苏淳 Department of Mathematics University of Science and Technology of China

Let {X_m} be a sequence of r.v., S, be its partial sum of the first nmembers, and H(t) be a function defined on (0, +∞) with the property of 0 详细信息

Let {X_m} be a sequence of r.v., S, be its partial sum of the first nmembers, and H(t) be a function defined on (0, +∞) with the property of 0 convergence.of tail probability series in the law of large numbers and In addition, we obtain a series of equivalent propositions and sufficiet propositions which overall reveal their inner relationships and solve those problems, posed by Soviet scholars recently. It is worth noting that there are some in our correct answers which are different from the forms of their problems.

关键词： number of times for overstepping generalized moment complete convergence.

Counterexamples to convergence.theorem of maximum-entropy clustering algorithm

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Science in China(Series F) 2003年第5期46卷 321-326页

作者：于剑石洪波黄厚宽孙喜晨程乾生 School of Computer and Information Technology Northern Jiaotong University Beijing China 100044 Department of Information Science School of Mathematical SciencePeking UniversityBeijing China 100871

In this paper, we surveyed the development of maximum-entropy clustering algorithm, pointed out that the maximum-entropy clustering algorithm is not new in essence, and constructed two examples to show that the iterative sequence given by the maximum-entropy clustering algorithm may not converge to a local minimum of its objective function, but a saddle point. Based on these results, our paper shows that the convergence.theorem of maximum-entropy clustering algorithm put forward by Kenneth Rose et al. does not hold in general cases.

关键词： entropy fixed point clustering algorithm convergence.

ON convergence.OF INTERPOLATED ITERATIVE METHOD OF GEOMETRICALLY NONLINEAR EQUATIONS OF CIRCULAR PLATES

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Science China Mathematics 1989年第3期32卷 316-327页

作者：郑晓静周又和 Department of Mechanics Lanzhou University

The convergence.of interpolated-iterative method, which is applied to solve von Karman ’sequations of circular plates, has been strictly proved for unilateral arbitrary loads. On thebasis of programme of selecting in... 详细信息

关键词： Karman plate equations interpolated-iterative method convergence.

An adaptive trust region method and its convergence

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Science China Mathematics 2002年第5期45卷 620-631页

作者：章祥荪张菊亮廖立志 1. Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong

In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence.results of the adaptive trust region method are *** results indicate that the new method is very efficient.

关键词： trust region method, unconstrained optimization, global convergence. superlinear convergence.

ON　convergence.AND　RATE　OF　convergence.OF　ALGORITHMS　IN　THE　MOVER－STAYER　MODEL

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Systems Science and Mathematical Sciences 1995年第1期8卷 46-51页

作者： WANG Dongqian Lawoko, C. R. O.(Department of Statistics, Massey University, Palmerston North, New Zealand) Massey University 新西兰

ＯＮＣＯＮＶＥＲＧＥＮＣＥＡＮＤＲＡＴＥＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＡＬＧＯＲＩＴＨＭＳＩＮＴＨＥＭＯＶＥＲ－ＳＴＡＹＥＲＭＯＤＥＬＷＡＮＧＤｏｎｇｑｉａｎ；Ｌａｗｏｋｏ，Ｃ．Ｒ．Ｏ．（ＤｅｐａｒｔｍｅｎｔｏｆＳｔ... 详细信息

ＯＮＣＯＮＶＥＲＧＥＮＣＥＡＮＤＲＡＴＥＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＡＬＧＯＲＩＴＨＭＳＩＮＴＨＥＭＯＶＥＲ－ＳＴＡＹＥＲＭＯＤＥＬＷＡＮＧＤｏｎｇｑｉａｎ；Ｌａｗｏｋｏ，Ｃ．Ｒ．Ｏ．（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，ＭａｓｓｅｙＵｎ...

关键词： Mover-stayer model algorithms convergence rate of convergence.

Self-tuning measurement fusion white noise deconvolution estimator with correlated noises

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Journal of Systems Engineering and Electronics 2010年第4期21卷 666-674页

作者： Xiaojun Sun Zili Deng Department of Automation Heilongjiang University Harbin 150080 R R. China

For the multisensor linear discrete time-invariant stochastic systems with correlated noises and unknown noise statistics,an on-line noise statistics estimator is presented by using the correlation *** it into the steady-state Riccati equation,the self-tuning Riccati equation is *** the Kalman filtering method,based on the self-tuning Riccati equation,a self-tuning weighted measurement fusion white noise deconvolution estimator is *** the dynamic error system analysis（DESA） method,it is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steadystate white noise deconvolution estimator in a realization,so that it has the asymptotic global optimality.A simulation example for Bernoulli-Gaussian input white noise shows its effectiveness.

关键词： multisensor information fusion measurement fusion self-tuning fuser white noise deconvolution asymptotic global optimality Kalman filtering convergence.

Quintic spline smooth semi-supervised support vector classification machine

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Journal of Systems Engineering and Electronics 2015年第3期26卷 626-632页

作者： Xiaodan Zhang Jinggai Ma Aihua Li Ang Li School of Mathematics and Physics University of Science and Technology Beijing Department of Mathematical Sciences Montclair State University

A semi-supervised vector machine is a relatively new learning method using both labeled and unlabeled data in classifi- cation. Since the objective function of the model for an unstrained semi-supervised vector machine is not smooth, many fast opti- mization algorithms cannot be applied to solve the model. In order to overcome the difficulty of dealing with non-smooth objective functions, new methods that can solve the semi-supervised vector machine with desired classification accuracy are in great demand. A quintic spline function with three-times differentiability at the ori- gin is constructed by a general three-moment method, which can be used to approximate the symmetric hinge loss function. The approximate accuracy of the quintic spiine function is estimated. Moreover, a quintic spline smooth semi-support vector machine is obtained and the convergence.accuracy of the smooth model to the non-smooth one is analyzed. Three experiments are performed to test the efficiency of the model. The experimental results show that the new model outperforms other smooth models, in terms of classification performance. Furthermore, the new model is not sensitive to the increasing number of the labeled samples, which means that the new model is more efficient.

关键词： semi-supervised support vector classification machine smooth quintic spline function convergence.