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An algorithm for solving new trust region subproblem with conic model

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Science China Mathematics 2008年第3期51卷 461-473页

作者： WANG JianYu ni qin Department of Mathematics Nanjing Xiaozhuang UniversityNanjing 211171China Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 210016China

The new trust region subproblem with the conic model was proposed in 2005, and was divided into three different cases. The first two cases can be converted into a quadratic model or a convex problem with quadratic constraints, while the third one is a nonconvex problem. In this paper, first we analyze the nonconvex problem, and reduce it to two convex problems. Then we discuss some dual properties of these problems and give an algorithm for solving them. At last, we present an algorithm for solving the new trust region subproblem with the conic model and report some numerical examples to illustrate the efficiency of the algorithm.

关键词： conic model trust-region subproblem nonconvex problem dual method 49K10 90C30

Rank-r decomposition of symmetric tensors

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Frontiers of Mathematics in China 2017年第6期12卷 1339-1355页

作者： Jie WEN qin ni Wenhuan ZHU College of Science Nanjing University of Aeronautics and Astronautics Nanjing 210016 China

An algorithm is presented for decomposing a symmetric tensor into a sum of rank-1 symmetric tensors. For a given tensor, by using apolarity, catalecticant matrices and the condition that the mapping matrices are commutative, the rank of the tensor can be obtained by iteration. Then we can find the generating polynomials under a selected basis set. The decomposition can be constructed by the solutions of generating polynomials under the condition that the solutions are all distinct which can be guaranteed by the commutative property of the matrices. Numerical examples demonstrate the efficiency and accuracy of the proposed method.

关键词： polynomial Symmetric tensor symmetric rank decomposition generating catalectieant matrix

A New Direct Search Method Based on Separable Fractional Interpolation Model

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Acta Mathematicae Applicatae Sinica 2016年第2期32卷 257-268页

作者： qin ni CUI JIANG HAO LIU College of Sciences Nanjing University of Aeronautics and Astronautics College of Sciences Nanjing University of Technology

In this paper, we propose a new separable fractional interpolation model which can be established by 2n interpolation points where n is the number of variables. Based on this model, a new direct search method is presented. In this method, a new iterate is determined by solving the fractional interpolation model in trust region. Under mild assumptions, the convergence results of this method are given and proved, Numerical experiments show that the new method is promising.

关键词： direct search method fractional interpolation model trust region

SEQUENTIAL CONVEX PROGRAMMING METHODS FOR SOLVING LARGE TOPOLOGY OPTIMIZATION PROBLEMS： IMPLEMENTATION AND COMPUTATIONAL RESULTS

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Journal of Computational Mathematics 2005年第5期23卷 491-502页

作者： qin ni Ch.Zillober K.Schittkowski Nanjing University of Aeronautics and Astronautics 210016 Nanjing China Department of Computer Science University of BayreuthD-95440 BayreuthGermany

In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.

关键词： Large scale optimization Topology optimization Sequential convex programming method Predictor-corrector interior point method Method of moving asymptotes

A New Method of Moving Asymptotes for Large-scale Linearly Equality-constrained Minimization

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Acta Mathematicae Applicatae Sinica 2011年第2期27卷 317-328页

作者： Hai-jun Wang qin ni Hao Liu College of Sciences China University of Mining and Technology Xuzhou 221008 China College of Sciences Nanjing University of Aeronautics and Astronautics Nanjing 210016 China College of Sciences Nanjing University of Technology Nanjing 210019 China

A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed. In this method, linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved. The numerical results show that the new method may be capable of processing some large scale problems.

关键词： method of moving asymptotes trust region linear search large scale linear equality constraints

MORPHOLOGY AND MECHAniCAL PROPERTIES OF POLYPROPYLENE WITH in situ FORMED POLYAMIDE-6 FIBRILS

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Chinese Journal of Polymer Science 2007年第6期25卷 599-607页

作者： Dong Liang qin Zhang Rong-ni Du Qiang Fu Colloge of Polymer Science and Materials Sichuan University State Key Laboratory of Polymer Materials Engineering Chengdu 610065 China

in situ Fibril formation of polyamide-6 （PA6） in isotropic polypropylene （iPP） was first fabricated using a slit die extrusion and hot stretching process. Then the prepared materials were subjected to injection molding in the temperature range higher than the melting temperature of iPP but lower than that of PA6. The obtained injection-molded samples were characterized via scanning electron microscopy （SEM）, differential scanning calorimetry （DSC） and two-dimensional wide- angle X-ray scattering （2D-WAXS）. Mechanical properties were also investigated. The SEM result shows that the optimum fibril formation could be only achieved in the range of 20 wt% to 30 wt% of PA6 content for the studied system. The fibril morphology changes along the sample thickness in the injection-molded bars. The fibril morphology in the skin layer was better than that in the core layer. 2D-WAXS results showed that the orientation of PP decreased with the increase of PA6 content, which indicated that the orientation of PP was confined by PA6 fibrils. Combined consideration of mechanical properties and morphology indicates that only PP/PA6 composites with 20 wt% of PA6 content show better properties because of the better fibril morphology and PP chain orientation.

关键词： in situ Fibril Morphology Property PA6 PP.

Surface-improvement mechanism of hybrid electrochemical discharge process using variable-amplitude pulses

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Chinese Journal of Aeronautics 2020年第10期33卷 2782-2793页

作者： Yan ZHANG Zhengyang XU Yu WANG qin ni Xiang LING School of Mechanical and Power Engineering Nanjing Tech UniversityNanjing 211800China College of Mechanical and Electrical Engineering Nanjing University of Aeronautics&AstronauticsNanjing 210016China AECC Sichuan Gas Turbine Research Establishment Chengdu 610500China

Superalloys are commonly used in aircraft manufacturing;however,the requirements for high surface quality and machining accuracy make them difficult to *** this study,a hybrid electrochemical discharge process using variable-amplitude pulses is proposed to achieve this *** this method,electrochemical machining(ECM)and electrical discharge machining(EDM)are unified into a single process using a sequence of variable-amplitude pulses such that the machining process realizes both good surface finish and high machining ***,the machining mechanism of the hybrid electrochemical discharge process using variable-amplitude pulses is *** mechanism is investigated by observations of machining waveforms and machined *** is found that,with a high-frequency transformation between high-and low-voltage waveforms within a voltage cycle,the machining mechanism is frequently transformed from EDM to pure *** critical discharge voltage is 40 *** pulse voltages greater than 40 V are applied,the machining accuracy is good;however,the surface has defects such as numerous discharge *** machining accuracy is maintained when high-voltage pulses are replaced by low-voltage pulses to enhance electrochemical *** results indicate that the proposed hybrid electrochemical discharge process using variable-amplitude pulses can yield high-quality surfaces with high machining accuracy.

关键词： Electrical discharge machining Electrochemical machining Hybrid machining Superalloy Variable-amplitude pulse

Lead Determination on MWNT/Nafion Composite Modified Glassy Carbon Electrodes

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Chinese Journal of Chemistry 2005年第11期23卷 1510-1514页

作者： XU, qin LIU, ni-Na ZHU, Jun-Jie Key Labororatory of Analytical Chemistry for Life Science Department of Chemistry Nanjing University Nanjing Jiangsu 210093 China

A composite material of nitric acid oxidized multiwalled carbon nanotube （MWNT） and Nation was prepared. Such composite was modified on a glassy carbon electrode to determine trace of lead by differential pulsed voltammetry. In pH=6.47 NaNO3 solution, Pb^2＋ ions were accumulated on the modified electrode at -0.4 V. Compared with a bare and a Nation film coated electrode, the composite coated GC electrode can reduce the accumulating potential and eliminate the toxic character of mercury. The calibration plots were linear at low concentration of 5.0× 10^-9-2.0× 10^-8 mol/L and high concentration of 2.5× 10^-8-5.0× 10^-6 mol/L. The performances characteristics indicate that the electrode can be used to determine trace Pb^2＋ ions.

关键词： composite lead electrochemistry differential pulsed voltammetry

GLOBAL CONVERGENCE AND IMPLEMENTATION OF NGTN METHOD FOR SOLVING LARGE-SCALE SMARSE NONLINEAR PROGRAMMING PROBLEMS

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Journal of Computational Mathematics 2001年第4期19卷 337-346页

作者： qin ni (Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China) 南京航空航天大学江苏南京 210016

An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and pos sesses Q-quadratic convergence rate. The global convergence of this new method is proved, the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.

关键词： Nonlinear programming Large-scale problem Sparse.