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作者： Wang, Xiao Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences PO Box 2719 Beijing 100190 China

In this paper, we propose a new trust region affine scaling method for nonlinear programming with simple bounds. Our new method is an interior-point trust region method with a new scaling technique. The scaling matrix depends on the distances of the current iterate to the boundaries, the gradient of the objective function and the trust region radius. This scaling technique is different from the existing ones. It is motivated by our analysis of the linear programming case. The trial step is obtained by minimizing the quadratic approximation to the objective function in the scaled trust region. It is proved that our algorithm guarantees that at least one accumulation point of the iterates is a stationary point. Preliminary numerical experience on problems with simple bounds from the CUTEr collection is also reported. The numerical performance reveals that our method is effective and competitive with the famous algorithm LANCELOT. It also indicates that the new scaling technique is very effective and might be a good alternative to that used in the subroutine fmincon from Matlab optimization toolbox. © 2013 Copyright Taylor and Francis Group, LLC.

关键词： Nonlinear programming

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Advances in biomolecular surface meshing and its applications to mathematical modeling

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Chinese Science Bulletin 2013年第16期58卷 1843-1849页

作者： CHEN MinXin LU BenZhuo Center for System Biology Department of Mathematics Soochow University State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics Academy of Mathematics and Systems Science National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences

In the field of molecular modeling and simulation, molecular surface meshes are necessary for many problems, such as molecular structure visualization and analysis, docking problem and implicit solvent modeling and simulation. Recently, with the developments of advanced mathematical modeling in the field of implicit solvent modeling and simulation, providing surface meshes with good qualities efficiently for large real biomolecular systems becomes an urgent issue beyond its traditional purposes for visualization and geometry analyses for molecular structure. In this review, we summarize recent works on this issue. First, various definitions of molecular surfaces and corresponding meshing methods are introduced. Second, our recent meshing tool, TMSmesh, and its performances are presented. Finally, we show the applications of the molecular surface mesh in implicit solvent modeling and simulations using boundary element method (BEM) and finite element method (FEM).

关键词：数学建模分子表面应用啮合生物表面网格分子结构分子建模

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A Cone Constrained Convex Program:Structure and Algorithms

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Journal of the Operations Research Society of China 2013年第1期1卷 37-53页

作者： Liqun Qi Yi Xu Ya-Xiang Yuan Xinzhen Zhang Department of Applied Mathematics The Hong Kong Polytechnic UniversityHung HomKowloonHong KongChina State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesZhong Guan Cun Donglu 55Beijing100190P.R.China Department of Mathematics School of ScienceTianjin UniversityTianjin300072China

In this paper,we consider the positive semi-definite space tensor cone constrained convex program,its structure and *** study defining functions,defining sequences and polyhedral outer approximations for this positive semidefinite space tensor cone,give an error bound for the polyhedral outer approximation approach,and thus establish convergence of three polyhedral outer approximation algorithms for solving this *** then study some other approaches for solving this structured convex *** include the conic linear programming approach,the nonsmooth convex program approach and the bi-level program *** numerical examples are presented.

关键词： Convex program Space tensor Positive semi-definiteness Cone Algorithms

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A PARAMETER-UNIFORM TAILORED FINITE POINT METHOD FOR SINGULARLY PERTURBED LINEAR ODE SYSTEMS＊

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Journal of Computational Mathematics 2013年第4期31卷 422-438页

作者： Houde Han J.J.H. Miller Min Tang Department of Mathematical Sciences Tsinghua University Beijing 100084 China Department of Mathematics Trinity College Dublin 2 Ireland Key Laboratory of Scientific and Engineering Computing Department of Mathematics and Institute of Natural Sciences Shanghai Jiao Tong University Shanghai 200240 China

In scientific applications from plasma to chemical kinetics, a wide range of temporal scales can present in a system of differential equations. A major difficulty is encountered due to the stiffness of the system and it is required to develop fast numerical schemes that are able to access previously unattainable parameter regimes. In this work, we consider an initial-final value problem for a multi-scale singularly perturbed system of linear ordi- nary differential equations with discontinuous coefficients. We construct a tailored finite point method, which yields approximate solutions that converge in the maximum norm, uniformly with respect to the singular perturbation parameters, to the exact solution. A parameter-uniform error estimate in the maximum norm is also proved. The results of numerical experiments, that support the theoretical results, are reported.

关键词： Tailored finite point method Parameter uniform Singular perturbation ODEsystem.

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Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrodinger Equation

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Communications in Computational Physics 2013年第7期14卷 393-411页

作者： Shanshan Jiang Lijin Wang Jialin Hong College of Science Beijing University of Chemical TechnologyBeijing 100029P.R.China School of Mathematical Sciences Graduate University of Chinese Academy of SciencesBeijing 100049P.R.China State Key Laboratory of Scientific and Engineering Computing Institute of ComputationalMathematics and Scientific/Engineering ComputingAcademy of Mathematics and System ScienceChinese Academy of SciencesP.O.Box 2719Beijing 100190P.R.China

In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochastic nonlinear Schrodinger *** is shown that the stochasticmulti-symplecticmethod preserves themultisymplectic structure,the discrete charge conservation law,and deduces the recurrence relation of the discrete *** experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.

关键词： Stochastic nonlinear Schrodinger equations stochasticmulti-symplectic Hamiltonian systems multi-symplectic integrators

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LOD-MS for Gross-Pitaevskii Equation in Bose-Einstein Condensates

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Communications in Computational Physics 2013年第6期14卷 219-241页

作者： Linghua Kong Jialin Hong Jingjing Zhang School of Mathematics and Information Science Jiangxi Normal UniversityNanchangJiangxi 330022P.R.China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and System ScienceChinese Academy of SciencesP.O.Box 2719Beijing 100190P.R.China School of Mathematics and Information Science Henan Polytechnic UniversityJiaozuoHenan 454000P.R.China

The local one-dimensional multisymplectic scheme(LOD-MS)is developed for the three-dimensional(3D)Gross-Pitaevskii(GP)equation in Bose-Einstein *** idea is originated from the advantages of multisymplectic integrators and from the cheap computational cost of the local one-dimensional(LOD)*** 3D GP equation is split into three linear LOD Schrodinger equations and an exactly solvable nonlinear Hamiltonian *** three linear LOD Schrodinger equations are multisymplectic which can be approximated by multisymplectic integrator(MI).The conservative properties of the proposed scheme are *** is ***,the scheme preserves the discrete local energy conservation laws and global energy conservation law if the wave function is variable *** is impossible for conventional MIs in nonlinear Hamiltonian *** numerical results show that the LOD-MS can simulate the original problems very *** are consistent with the numerical analysis.

关键词： LOD-MS Gross-Pitaevskii equation local one-dimensional method midpoint method conservation laws

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RETRACTED ARTICLE: Preface to the special issue on “Practical methods and rigorous theories in numerical algebra and scientific computing”

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Journal of engineering Mathematics 2014年第1期91卷 211-211页

作者： Bai, Zhong-Zhi Duff, Iain S. State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing People’s Republic of China R18 Rutherford Appleton Laboratory Harwell Oxford Campus Didcot UK

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A Subspace Version of the Powell–Yuan Trust-Region Algorithm for Equality Constrained Optimization

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Journal of the Operations Research Society of China 2013年第4期1卷 425-451页

作者： Geovani Nunes Grapiglia Jinyun Yuan Ya-xiang Yuan Departamento de Matemática Universidade Federal do ParanáCentro PolitécnicoCx.postal 19.08181531-980CuritibaParanáBrazil The Capes Foundation Ministry of Education of BrazilCx.postal 25070.040-020BrasíliaDistrito FederalBrazil State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesZhongguancundonglu 55Beijing 100190P.R.China

This paper studied subspace properties of the Celis–Dennis–Tapia(CDT)subproblem that arises in some trust-region algorithms for equality constrained opti*** analysis is an extension of that presented by Wang and Yuan(***.104:241–269,2006)for the standard trust-region *** suitable conditions,it is shown that the trial step obtained from the CDT subproblem is in the subspace spanned by all the gradient vectors of the objective function and of the constraints computed until the current *** on this observation,a subspace version of the Powell–Yuan trust-region algorithm is proposed for equality constrained optimization problems where the number of constraints is much lower than the number of variables. The convergence analysis is given and numerical results arealso reported.

关键词： Constrained optimization Trust-region methods Subspace methods

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Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction

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Physical Review E 2013年第1期87卷 013307-013307页

作者： Zhenli Xu []Department of Mathematics Institute of Natural Sciences and Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China

Electrostatic polarization is important in many nano- and micro-scale physical systems such as colloidal suspensions, biopolymers, and nanomaterials assembly. The calculation of polarization potential requires an efficient algorithm for solving 3D Poisson's equation. We have developed a useful image charge method to rapid evaluation of the Green's function of the Poisson's equation in the presence of spherical dielectric discontinuities. This paper presents an extensive study of this method by giving a convergence analysis and developing a coarse-graining algorithm. The use of the coarse graining could reduce the number of image charges to around a dozen, by 1–2 orders of magnitude. We use the algorithm to investigate the interaction force between likely charged spheres in different dielectric environments. We find the size and charge asymmetry leads to an attraction between like charges, in agreement with existing results. Furthermore, we study three-body interactions and find, in the presence of an external interface, that the interaction force depends on the curvature of the interface and performs a nonmonotonic electrostatic force.

关键词： ELECTROSTATICS INTERFACES (Physical sciences) POLARIZATION (Electricity) POISSON'S equation NONMONOTONIC logic GREEN'S functions

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Recent Development in Symmetries and Integrability of Difference Equations

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Frontiers of Mathematics in China 2013年第5期8卷 999-1000页

作者： Xingbiao HU Qingping LIU Senyue LOU Changzheng QU Youjin ZHANG Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Department of Mathematics China University of Mining and Technology~Beijing i00083 China Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai 200062 China Faculty of Sciences Ningbo University Ningbo 315211 China Center for Nonlinear Studies Ningbo University Ningbo 315211 China Department of Mathematical Sciences Tsinghua University Beijing 100084 China

Difference equations or discrete systems are mathematical models of various fields such as physics, chemistry, biology, and economics and have been subjects of extensive study of both pure mathematicians and applied mathematicians. Through its interaction with modern integrable systems, the theory of difference equations is enriched greatly and has been undergoing a rapid development. SIDE-10, the tenth of a series of biennial conferences devoted to Symmetries and Integrability of Difference Equations and related topics, was held during 10-16 June, 2012 at Ningbo, China. It was sponsored and supported by the National Natural Science Foundation of China, Ningbo Association of Science and Technology, Ningbo University, Academy of Mathematics and Systems Science of Chinese Academy of Sciences, China University of Mining and Technology （Beijing）, Tsinghua University, and Shanghai University. The conference attracted over 100 participants from more than a dozen of countries. During the conference, 44 contributed talks were arranged and the topics covered by the meeting include

关键词： Recent Development Symmetries

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