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The expansion problem of anti-symmetric matrix under a linear constraint and the optimal approximation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2006年第1期197卷 44-52页

作者： Gong, Lisha Hu, Xiyan Zhang, Lei Hunan Univ Coll Math & Econometr Changsha 410082 Peoples R China

This paper mainly discusses the following two problems: Problem I. Given A is an element of R-nxm, B is an element of R-mxm, X-0 is an element of ASR(qxq) (the set of q x q anti-symmetric matrices), find X is an element of ASR(nxn) such that A(T)XA = B, X-0 = X([1 : q]), where X([1 : q]) is the q x q leading principal submatrix of matrix X. Problem II. Given X* is an element of R-nxn, find (X) over cap is an element of S-E such that parallel to X* - (X) over cap parallel to = min(X is an element of SE) parallel to X* - X parallel to, where parallel to center dot parallel to is the Frobenius norm, and SE is the solution set of Problem I. The necessary and sufficient conditions for the existence of and the expressions for the general solutions of Problem I are given. Moreover, the optimal approximation solution, an algorithm and a numerical example of Problem II are provided. (c) 2005 Elsevier B.V. All rights reserved.

关键词： anti-symmetric matrix linear constraint Frobenius norm optimal approximation

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Global optimization over linear constraint non-convex programming problem

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Journal of Harbin Institute of Technology(New Series) 2005年第6期12卷 650-655页

作者：张贵军吴惕华叶蓉杨海清 College of Information Zhejiang University of Technology Hangzhou 310032 China Hebei Academy of Sciences Shijiazhuang 050081 China

A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programming problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.

关键词： global optimization linear constraint steady state genetic algorithms extremes encode convex crossover

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TESTING A linear constraint FOR MULTINOMIAL CELL FREQUENCIES AND DISEASE SCREENING

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ANNALS OF STATISTICS 1978年第4期6卷 904-909页

作者： KLOTZ, JH

For comparing two disease screening procedures with economic costs assigned to administration, false positives, and false negatives, the problem of testing a linear cell frequency constraint ∑i=1Kaipi≦0 arises with the multinomial (n,(p1,p2,⋯,pK)) model. An ad hoc statistic based upon the estimate of the pi values, ∑i=1KaiXi/n, is compared with the likelihood ratio statistic −2ln⁡λ, the latter having an interesting form. For local (contiguous) alternatives the two statistics have similar large sample properties. However, the likelihood ratio statistic has greater large deviation efficiency for fixed alternatives and is recommended.

关键词： 62F05 62P10 disease screening efficiency Information large deviations likelihood ratio test linear constraint Multinomial testing

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Reducing the coefficients of a two-dimensional integer linear constraint

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12th International Workshop on Combinatorial Image Analysis

作者： Charrier, Emilie Buzer, Lilian Laboratory CNRS-UMLV-ESIEE UMR 8049 France ESIEE Cité DESCARTES 93160 Noisy le Grand CEDEX 2 boulevard Blaise Pascal France DGA/D4S/MRIS France

ISBN: (纸本)9783540782742

Let us consider a two-dimensional linear constraint C of the form ax + by <= c with integer coefficients and such that vertical bar a vertical bar <= vertical bar b vertical bar. A constraint C' of the form a'x + b'y <= c' is equivalent to C relative to a domain iff all the integer points in the domain satisfying C satisfy C' and all the integer points in the domain not satisfying C do not satisfy C'. This paper introduces a new method to transform a constraint C into an equivalent constraint C' relative to a domain defined by {(x , y) vertical bar h <= x <= h + D} such that the absolute values of a' and b' do not exceed D. Our method achieves a O(log(D)) time complexity and it can operate when the constraints coefficients are real values with the same time complexity. This transformation can be used to compute the convex hull of the integer points which satisfy a system of n two-dimensional linear constraints in O(n log(D)) time where D represents the size of the solution space. Our algorithm uses elementary statements from number theory and leads to a simple and efficient implementation.

关键词： linear constraint integer convex hull Bezout identity logarithmic time complexity continued fraction

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A Modified Spectral Phase Conjugation Algorithm for Quadratic Programming with linear constraint Problems-application to Municipal Solid Waste Management

A Modified Spectral Phase Conjugation Algorithm for Quadrati...

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2017 2nd International Conference on Applied Mathematics, Simulation and Modelling(AMSM2017)

作者： Xiang-ming KONG Dong-lin WANG Beijing Polytechnic

In this study,a modified spectral phase conjugation algorithm(MSPCA) for quadratic programming with linear constraint(QPLC) is developed for waste-management *** is applied to a municipal solid waste(MSW) management *** results indicate that reasonable solutions have been generated for supporting MSW management,which supply more information for managers to make decisions.

关键词： Phase conjugation Quadratic programming Waste management Decision making linear constraint

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Generalized Least Squares Estimate of Error Self-correlation Regression Model Under the linear constraint

Generalized Least Squares Estimate of Error Self-correlation...

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作者： Xu Rongfei Department of Mathematics Nanjing Normal University Taizhou college

In this paper, we use the generalized least-squares estimator to give the parameter estimation formula of the error self-correlation regression model under linear constraint, at the same time, the size of the sum of squares for residuals of the model is compared to that of the unconstrained, this conclusion has some theoretical and practical value for further research and application of the model.

关键词： linear constraint Error Self-correlation Regression Model Generalized least squares estimate

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linear Differential Pursuit Game with Impulse Control and linear Integral constraint of Controls of Players

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Journal of Mathematical Sciences (United States) 2020年第1期245卷 23-39页

作者： Tukhtasinov, M. National University of Uzbekistan named after M. Ulugbek Tashkent Uzbekistan

For a linear differential pursuit-evasion game, we propose sufficient termination conditions in the case where one of players applies impulse controls whereas the other applies controls with “linear constraints” of integral type. We indicate methods for finding controls of the pursuer that provide termination of the pursuit in a finite time. Finally, we give examples that illustrate the results obtained. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： 49N70 49N75 admissible control Dirac function evader impulse control linear constraint pursuer pursuit resolving function terminal set

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MST based clustering method with linear constraint

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Moshi Shibie yu Rengong Zhineng/Pattern Recognition and Artificial Intelligence 2002年第4期15卷 494-497页

作者： Wang, Min Zhou, Chenghu Pei, Tao Luo, Jiancheng Lab. of Environ. Info. Syst. Chinese Acad. of Sci. Beijing 100101 China

A MST based clustering method with linear constraint is proposed, whose aim is to clustering the objects distributing densely and linearly in space. The algorithm restricts the selection of the splitting edges of the MST with linear threshold, which tries to cut off one sub-tree whose linear rate exceeds the threshold every splitting. The algorithm will stop when all the suitable sub-trees are cut off, and the remaining sub-trees are discarded. The effectiveness and practicality of our methods are validated by clustering the constructed data and the earthquake data.

关键词： Clustering linear constraint Minimal spanning tree Spatial data mining

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Temperature and Emissivity Retrievals From Hyperspectral Thermal Infrared Data Using linear Spectral Emissivity constraint

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2011年第4期49卷 1291-1303页

作者： Wang, Ning Wu, Hua Nerry, Francoise Li, Chuanrong Li, Zhao-Liang Chinese Acad Sci State Key Lab Resources & Environm Informat Syst Inst Geog Sci & Nat Resources Res Beijing 100101 Peoples R China Chinese Acad Sci Grad Univ Beijing 100049 Peoples R China UdS Image Sci Comp Sci & Remote Sensing Lab LSIIT CNRS F-67412 Illkirch Graffenstaden France Chinese Acad Sci Acad Optoelect Beijing 100080 Peoples R China

Owing to the ill-posed problem of radiometric equations, the separation of land surface temperature (LST) and land surface emissivity (LSE) from observed data has always been a troublesome problem. On the basis of the assumption that the LSE spectrum can be described by a piecewise linear function, a new method has been proposed to retrieve LST and LSE from atmospherically corrected hyperspectral thermal infrared data using linear spectral emissivity constraint. Comparisons with the existing methods found in literature show that our proposed method is more noise immune than the existing methods. Even with a NE Delta T of 0.5 K, the rmse of LST is observed to be only 0.16 K, and that of LSE is 0.006. In addition, our proposed method is simple and efficient and does not encounter the problem of singular values unlike the existing methods. As for the impact of the atmosphere, the results show that our proposed method performs well with the uncertainty of the atmospheric downwelling radiance but suffers from the inaccuracy of the atmospheric upwelling radiance and atmospheric transmittance, which implies that an accurate atmospheric correction is still needed to convert the radiance measured at the satellite level to the at-ground radiance. To validate the proposed method, a field experiment was conducted, and the results show that 80% of the samples have an accuracy of LST within 1 K and that the mean values of LSE are accurate to 0.01.

关键词： Emissivity hyperspectral thermal infrared (TIR) land surface temperature (LST) linear constraint retrieval

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A generalized maximum correntropy based constraint adaptive filtering: constraint-forcing and performance analyses

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ISA TRANSACTIONS 2025年 157卷 199-212页

作者： Zhao, Ji Li, Wenyue Li, Qiang Zhang, Hongbin Southwest Univ Sci & Technol Sch Informat Engn Mianyang 621010 Sichuan Peoples R China Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Sichuan Peoples R China

The quadratic cost functions, exemplified by mean-square-error, often exhibit limited robustness and flexibility when confronted with impulsive noise contamination. In contrast, the generalized maximum correntropy (GMC) criterion, serving as a robust nonlinear similarity measure, offers superior performance in such scenarios. In this paper, we develop a recursive constrained adaptive filtering algorithm named recursive generalized maximum correntropy with a forgetting factor (FF-RCGMC). This algorithm integrates the exponential weighted GMC criterion with a linear constraint framework based on least-squares. However, the lack of constraint information during the learning process may lead to divergence or malfunctioning of FF-RCGMC after a certain number of iterations because of round-off errors. To rectify this deficiency, we introduce a constraint-forcing strategy into FF-RCGMC, resulting in a more stable variant termed robust type constraint-forcing FF-RCGMC (CFFF-RCGMC). In the context of CFFF-RCGMC, we embark on a thorough examination of its computational burden, encompassing both mean and mean-square stability analyses, along with an in-depth exploration of its transient and steady-state filtering characteristics under a set of plausible assumptions. Our simulation- based evaluations, specifically tailored for system identification tasks within non-Gaussian noisy environments, unequivocally underscore the excellent performance of CFFF-RCGMC when against its relevant algorithmic counterparts.

关键词： linear constraint Adaptive filtering Generalized correntropy System identification Outlier

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