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Finding Symmetry Groups of Some Quadratic Programming Problems

Numerical Mathematics(Theory,Methods and Applications) 2023年第2期16卷 370-392页

作者： Anton V.Eremeev Alexander S.Yurkov Sobolev Institute of Mathematics SB RAS Omsk DepartmentOmskRussia Omsk Scientific Center SB RAS(Institute of Radiophysics and Physical Electronics) OmskRussia

Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear *** particular,a knowledge of the symmetries may help decrease the problem dimension,reduce the size of the search space by means of linear *** the previous studies of symmetries in the mathematical programming usually dealt with permutations of coordinates of the solutions space,the present paper considers a larger group of invertible linear *** study a special case of the quadratic programming problem,where the objective function and constraints are given by quadratic *** formulate conditions,which allow us to transform the original problem to a new system of coordinates,such that the symmetries may be sought only among orthogonal *** particular,these conditions are satisfied if the sum of all matrices of quadratic forms,involved in the constraints,is a positive definite *** describe the structure and some useful properties of the group of symmetries of the *** that,the methods of detection of such symmetries are outlined for different special cases as well as for the general case.

关键词： Non-convex programming orthogonal transformation symmetry group Lie group

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An iterative algorithm of NWTLS-EC for three dimensional-datum transformation with large rotation angle

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Geodesy and Geodynamics 2014年第4期5卷 38-48页

作者： Hu Chuan Chen Yi College of Surveying and Geo-Informatics Tongji University Key Laboratory of Advanced Surveying Engineering of National Administration of Surveying Mapping and Geoinformation

The Gauss-Markov （GM） model and the Errors-in-Variables （EIV） model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation errors in original coordinates system are also taken into account, the latter is more accurate and reasonable than the former. Although the Weighted Total Least Squares （WTLS） technique has been intro- duced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance- Covariance Matrix （VCM） of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account. Because the 3D datum transformation with large rotation angle is a non- linear problem, the WTLS is no longer suitable in this ease. In this contribution, we suggested the nonlinear WTLS adjustments with equality constraints （NWTLS-EC） for 3D datum transformation with large rotation an- gle, which removed the particular structure restriction on the VCM. The Least Squares adjustment with Equality （LSE） constraints is employed to solve NWTLS-EC as the nonlinear model has been linearized, and an iterative algorithm is proposed with the LSE solution. A simulation study of 3D datum transformation with large rotation angle is given to insight into the feasibility of our algorithm at last.

关键词： nonlinear weighted total least squares equality constraints 3D datum transformation heterosce-dastic and correlated orthogonal transformation

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Stiffness Analysis of Spherical Parallel Mechanism U_(P+R) with 2-DOF

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Journal of Harbin Institute of Technology(New Series) 2013年第4期20卷 41-47页

作者： Yu-Lin Zhou Long Yang Bo Li Da-Xing Zeng Feng Gao School of Mechanical Engineering Yanshan University XCMG Xuzhou Truck-Mounted Crane Co. Ltd. State Key Laboratory of Mechanical System and Vibration Shanghai Jiaotong University

As one of the typical less-mobility parallel mechanisms,the spherical parallel mechanism U_(P + R) with two degrees of freedom(2-DOF)possess high order overconstraints,and the calculation of its stiffness is partly different with general parallel mechanisms owing to the bars in each branch are assumed to be *** means of small deformation superposition principle,the relationship between the angle displacement and line displacement of moving platform and the forces acted on the branches were derived *** on the results of static analysis,the relationship between the applied force,the line displacement and the angle displacement of the mechanism was set *** then the stiffness matrix was *** six principal stiffness of the mechanism and the corresponding directions were achieved by the orthogonal *** numerical calculation was performed and the results showed that the principal stiffness and directions are varied with the pose-position of the mechanism,and the principal stiffness is gradually enlarged when it is far away from the *** addition,the torsion stiffness is much greater and the line deformation stiffness is smaller,the difference between the two parts is *** research content of this paper supplies the theoretical foundation for the further engineering design and application of the spherical parallel mechanism.

关键词： spherical parallel mechanism static stiffness orthogonal transformation line displacement angle displacement

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On Quadratic Lyapunov Function of Planar Systems

On Quadratic Lyapunov Function of Planar Systems

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第二十届中国控制会议

作者： Daizhan Cheng Institute of Systems Science, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing 100080, P.R.China

＜正＞This paper considers the problem of finding a common quadratic Lyapunov function for a set of planar systems. The main contribution of this paper is to figure out the set of quadratic Lyapunov functions for a given stable planar system. Then a necessary and sufficient condition for a set of plane systems to share a common quadratic Lyapunov function is obtained consequently. It is not only easily verifiable but also constructive. It provides a method to construct all common quadratic Lyapunov functions. As an application, higher dimensional cases are also considered.

关键词： Switch system common quadratic Lyapunov function orthogonal transformation solvable Lie algebra quasi-flag

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A New Parallel Algorithm for Eigenstructure Assignment

A New Parallel Algorithm for Eigenstructure Assignment

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第二十四届中国控制会议

作者： Li Shiguang, Chen Dayue, Cai Liangbin(Department of Instrument Engineering,Shanghai Jiaotong University. 200030)

＜正＞ For conventional eigenstructure assignment technique. the strict constraint of complete difference between open-loop poles and closed-loop ones is required and the high cost of the resulting Sylvester matrix equations computation under the condition of higher dimensions is encountered. One parallel algorithm of eigenstructure assignment is presented in this paper. The combination of orthogonal transformation with partition block technique is employed to transform one high order matrix equations into two lower order ones. Parallel computing is used to solve two reduced-order matrix equations in order to decrease computing cost. Moreover. partial pole assignment is implemented due to the fact that the sufficient condition in which there exists solution to transformed matrix equations is relaxed in comparison with the sufficient condition of initiative matrix equations solution existence. Parameterized eigenvector is determined through the error 2-norm between desired eigenvector and objective one is minimized while the exactly assigned eigenvalues are guaranteed. Two numerical examples indicate that the presented algorithm for eigenstructure assignment is effective.

关键词： eigenstructure assignment parallel algorithm Parameterized eigenvector orthogonal transformation 2-norm

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