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A Homogeneous smoothing-type algorithm for Symmetric Cone Linear Programs

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 647-662页

作者： Wei-Zhe GU Zheng-Hai HUANG Department of Mathematics School of ScienceTianjin University

In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program （（SCLP） for short） by making use of an augmented system of its optimality conditions. The algorithm only needs to solve one system of linear equations and to perform one line search at each iteration. It is proved that the algorithm is globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, the algorithm may correctly detect solvability of （SCLP）. Furthermore, if （SCLP） has a solution, then the algorithm will generate a solution of （SCLP）, and if the problem is strongly infeasible, the algorithm will correctly detect infeasibility of （SCLP）.

关键词： linear program symmetric cone Euclidean Jordan algebra smoothing algorithm global conver-gence

smoothing Newton algorithm for Linear Programming over Symmetric Cones

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Transactions of Tianjin University 2009年第3期15卷 216-221页

作者：刘晓红倪铁 School of Sciences Tianjin University

By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm... 详细信息

关键词： linear programming symmetric cone Euclidean Jordan algebra smoothing algorithm

Variable structure multiple model fixed-interval smoothing

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Chinese Journal of Aeronautics 2023年第2期36卷 139-148页

作者： Bolun ZHANG Yongxin GAO Zhansheng DUAN Faculty of Electronic and Information Engineering School of Automation Science and EngineeringXi’an Jiaotong UniversityXi'an 710049China

This paper focuses on fixed-interval smoothing for stochastic hybrid *** the truth-mode mismatch is encountered,existing smoothing methods based on fixed structure of model-set have significant performance degradation and are *** develop a fixedinterval smoothing method based on forward-and backward-filtering in the Variable Structure Multiple Model(VSMM)framework in this *** propose to use the Simplified Equivalent model Interacting Multiple Model(SEIMM)in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters,and design a re-filtering procedure in the model-switching stage to enhance the estimation *** improve the computational efficiency,we make the basic model-set adaptive by the Likely-Model Set(LMS)*** turns out that the smoothing performance is further improved by the LMS due to less competition among *** results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.

关键词： Fixed-interval smoothing Model-set adaptation Multiple model estimation smoothing algorithm Variable structure

EXTENSION OF smoothing NEWTON algorithmS TO SOLVE LINEAR PROGRAMMING OVER SYMMETRIC CONES

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Journal of Systems Science & Complexity 2011年第1期24卷 195-206页

作者： Zhenghai HUANG Xiaohong LIU Department of Mathematics School of Science Tianjin University Tianjin 300072 China

There recently has been much interest in studying some optimization problems over symmetric cones. This paper deals with linear programming over symmetric cones （SCLP）. The objective here is to extend the Qi-Sun-Zhou＇s smoothing Newton algorithm to solve SCLP, where characterization of symmetric cones using Jordan algebras forms the fundamental basis for our analysis. By using the theory of Euclidean Jordan algebras, the authors show that the algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results for solving the second-order cone programming are also reported.

关键词： Euclidean Jordan algebra linear programming smoothing algorithm symmetric cone.

An Improved Unsupervised Approach to Word Segmentation

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China Communications 2015年第7期12卷 82-95页

作者： WANG Hanshi HAN Xuhong LIU Lizhen SONG Wei YUAN Mudan Information and Engineering College Capital Normal University Beijing Bayi High School

ESA is an unsupervised approach to word segmentation previously proposed by Wang, which is an iterative process consisting of three phases: Evaluation, Selection and Adjustment. In this article, we propose Ex ESA, the extension of ESA. In Ex ESA, the original approach is extended to a 2-pass process and the ratio of different word lengths is introduced as the third type of information combined with cohesion and separation. A maximum strategy is adopted to determine the best segmentation of a character sequence in the phrase of Selection. Besides, in Adjustment, Ex ESA re-evaluates separation information and individual information to overcome the overestimation frequencies. Additionally, a smoothing algorithm is applied to alleviate sparseness. The experiment results show that Ex ESA can further improve the performance and is time-saving by properly utilizing more information from un-annotated corpora. Moreover, the parameters of Ex ESA can be predicted by a set of empirical formulae or combined with the minimum description length principle.

关键词： word segmentation character sequence smoothing algorithm maximum strategy