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A ROBUST SQP METHOD BASED ON A SMOOTHING APPROXIMATE PENALTY FUNCTION FOR INEQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems Science & Complexity 2002年第1期15卷 102-112页

作者： zhangJuliang zhangxiangsun InstituteofAppliedMathematics AcademyofMathematicsandSystemsScienceChineseAcademyofSciencesBeijing100080China InstituteofAppliedMathematics AcademyofMathematicsandSystemsScienceChineseAcademyofSci

A robust SQP method, which is analogous to Facchinei’s algorithm, is introduced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. In addition, the algorithm employs a differentiable approximate exact penalty function as a merit function. Unlike the merit function in Facchinei’s algorithm, which is quite complicated and is not easy to be implemented in practice, this new merit function is very simple. As a result, we can use the Facchinei’s idea to construct an algorithm which is easy to be implemented in practice.

关键词：非线性最优问题 SQP方法整体收敛

REMARKS ON NETWORK COMMUNITY PROPERTIES

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Journal of Systems Science & Complexity 2008年第4期21卷 637-644页

作者： Jiguang WANG Yuqing QIU Ruisheng WANG xiangsun zhang Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Graduate University of the Chinese Academy of Sciences Beijing 100049 China. School of Information Renmin University of China Beijing 100872 China. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China.

这篇论文以一个社区是最小的在下面条件在复杂网络研究讨论一个流行社区定义，也就是说，社区不能被分成几个更小的社区或裂口并且与另外的网络元素重新组织进新社区。结果提供为社区鉴定的量的措施的进一步的优化计算能在上被认识到的... 详细信息

这篇论文以一个社区是最小的在下面条件在复杂网络研究讨论一个流行社区定义，也就是说，社区不能被分成几个更小的社区或裂口并且与另外的网络元素重新组织进新社区。结果提供为社区鉴定的量的措施的进一步的优化计算能在上被认识到的一个底。

关键词：网络论坛社区优化算法模块密度

RECOGNITION OF STRUCTURE SIMILARITIES IN PROTEINS

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Journal of Systems Science & Complexity 2008年第4期21卷 665-675,F0003页

作者： Lin WANG Yuqing QIU Jiguang WANG xiangsun zhang Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Graduate School of the Chinese Academy of Sciences Beijing 100049 China. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China.

蛋白质褶层结构是比它的氨基酸顺序保存并且仔细与生物功能联系了推测蛋白质结构的类似是在结构的生物学的一个基本问题并且在蛋白质褶层分类，褶层功能推理，和蛋白质结构起一个关键作用的更多预言。大进步为认为结构的类似被建议了在... 详细信息

蛋白质褶层结构是比它的氨基酸顺序保存并且仔细与生物功能联系了推测蛋白质结构的类似是在结构的生物学的一个基本问题并且在蛋白质褶层分类，褶层功能推理，和蛋白质结构起一个关键作用的更多预言。大进步为认为结构的类似被建议了在这块地和许多方法里在最近的年里被取得了，包括为蛋白质结构比较，从数据库的蛋白质结构的检索，和 ligand 绑定的方法地点比较。大多数那些方法能在万维网上是可得到的，但是所有方法的评估仍然是一个难问题。这篇论文为结构类似总结一些流行方法和最近的方法，包括结构排列，蛋白质结构检索，和 ligand 绑定地点排列。

关键词：蛋白质氨基酸生物机能结构

Mathematical Model and Algorithm for Link Community Detection in Bipartite Networks

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American Journal of Operations Research 2015年第5期5卷 421-434页

作者： Zhenping Li Shihua zhang xiangsun zhang School of Information Beijing Wuzi University Beijing China National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Beijing China

In the past ten years, community detection in complex networks has attracted more and more attention of researchers. Communities often correspond to functional subunits in the complex systems. In complex network, a node community can be defined as a subgraph induced by a set of nodes, while a link community is a subgraph induced by a set of links. Although most researches pay more attention to identifying node communities in both unipartite and bipartite networks, some researchers have investigated the link community detection problem in unipartite networks. But current research pays little attention to the link community detection problem in bipartite networks. In this paper, we investigate the link community detection problem in bipartite networks, and formulate it into an integer programming model. We proposed a genetic algorithm for partition the bipartite network into overlapping link communities. Simulations are done on both artificial networks and real-world networks. The results show that the bipartite network can be efficiently partitioned into overlapping link communities by the genetic algorithm.

关键词： Bipartite Network Link Community Quantity Function Integer Programming Genetic Algorithm

A Neural Network Algorithm for the (m,d)-Coloring Problem of a Graph

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A Neural Network Algorithm for the (m,d)-Coloring Problem of...

The LBFGS quasi-Newtonian method for molecular modeling prion AGAAAAGA amyloid fibrils

中国运筹学会第七届学术交流会

作者： zhang xiangsun LI Zhenping ZHOU Wenfeng Academy of Mathematics and System Sciences,CAS,Beijing 100080, China Beijing Materials Institute, Beijing 101149, China.

In this paper we discuss the algorithm of (m,d)-coloring problem of agraph, and give a four-layer neural network algorithm. Using this algorithm, we cansuccessively find an optimal (m,d)-coloring of the graph with given circular chromaticnumber;moreover we can use this algorithm to find the approximate circular chro-matic number of a graph.

关键词： Network (m,d)-Coloring Graph

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Natural Science 2012年第12期4卷 1097-1108页

作者： Jiapu zhang Yating Hou Yiju Wang Changyu Wang xiangsun zhang Centre for Informatics and Applied Optimization & Graduate School of Sciences Information Technology and Engineering The University of Ballarat Victoria Australia Institute of Applied Mathematics Academia Sinica Beijing China School of Management Science Qufu Normal University Rizhao China

Experimental X-ray crystallography, NMR (Nuclear Magnetic Resonance) spectroscopy, dual polarization interferometry, etc. are indeed very powerful tools to determine the 3-Dimensional structure of a protein (including the membrane protein);theoretical mathematical and physical computational approaches can also allow us to obtain a description of the protein 3D structure at a submicroscopic level for some unstable, noncrystalline and insoluble proteins. X-ray crystallography finds the X-ray final structure of a protein, which usually need refinements using theoretical protocols in order to produce a better structure. This means theoretical methods are also important in determinations of protein structures. Optimization is always needed in the computer-aided drug design, structure-based drug design, molecular dynamics, and quantum and molecular mechanics. This paper introduces some optimization algorithms used in these research fields and presents a new theoretical computational method—an improved LBFGS Quasi-Newtonian mathematical optimization method—to produce 3D structures of prion AGAAAAGA amyloid fibrils (which are unstable, noncrystalline and insoluble), from the potential energy minimization point of view. Because the NMR or X-ray structure of the hydrophobic region AGAAAAGA of prion proteins has not yet been determined, the model constructed by this paper can be used as a reference for experimental studies on this region, and may be useful in furthering the goals of medicinal chemistry in this field.

关键词： Protein 3D Structure Computational Approaches Optimization Method Molecular Modelling Prion AGAAAAGA Amyloid Fibrils

ON A NEW GRADIENT PROJECTION METHOD

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