We consider a class of ABS type algorithms for solving system of linear inequalities, where the number of inequalities does not exceed the number of variables.
The known Fourier-Chernikov algorithm of linear inequality system convolution is complemented with an original procedure of all dependent (redundant) inequalities deletion. The concept of “almost dependent” inequali...The known Fourier-Chernikov algorithm of linear inequality system convolution is complemented with an original procedure of all dependent (redundant) inequalities deletion. The concept of “almost dependent” inequalities is defined and an algorithm for further reducing the system by deletion of these is considered. The concluding algorithm makes it possible to hold actual-time convolution of a general inequality system containing up to 50 variables with the rigorous method of dependent inequalities deletion and up to 100 variables with the approximate method of one. The main application of such an approach consists in solving linear inequality system in an explicit form. These results are illustrated with a series of computer experiments.展开更多
Linear Least Square (LLS) is an approach for modeling regression analysis, applied for prediction and quantification of the strength of relationship between dependent and independent variables. There are a number of m...Linear Least Square (LLS) is an approach for modeling regression analysis, applied for prediction and quantification of the strength of relationship between dependent and independent variables. There are a number of methods for solving the LLS problem but as soon as the data size increases and system becomes ill conditioned, the classical methods become complex at time and space with decreasing level of accuracy. Proposed work is based on prediction and quantification of the strength of relationship between sugar fasting and Post-Prandial (PP) sugar with 73 factors that affect diabetes. Due to the large number of independent variables, presented problem of diabetes prediction also presented similar complexities. ABS method is an approach proven better than other classical approaches for LLS problems. ABS algorithm has been applied for solving LLS problem. Hence, separate regression equations were obtained for sugar fasting and PP severity.展开更多
This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations.The present methodcuts down computing time enormously and greatly, promotes...This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations.The present methodcuts down computing time enormously and greatly, promotes the efficiency of the elasto-plastic andlysis for large scale structures.展开更多
As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many o...As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.展开更多
This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations The present method cuts down computing time enormously and greatly promote...This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations The present method cuts down computing time enormously and greatly promotes the efficiency of the elasto-plastic analvsis for large scale structures展开更多
基金Work supported by the Science Foundation of State Education Commission of China and CNR of Italy.
文摘We consider a class of ABS type algorithms for solving system of linear inequalities, where the number of inequalities does not exceed the number of variables.
文摘The known Fourier-Chernikov algorithm of linear inequality system convolution is complemented with an original procedure of all dependent (redundant) inequalities deletion. The concept of “almost dependent” inequalities is defined and an algorithm for further reducing the system by deletion of these is considered. The concluding algorithm makes it possible to hold actual-time convolution of a general inequality system containing up to 50 variables with the rigorous method of dependent inequalities deletion and up to 100 variables with the approximate method of one. The main application of such an approach consists in solving linear inequality system in an explicit form. These results are illustrated with a series of computer experiments.
基金supported by National Natural Science Foundation of China(61403254,61374039,61203143)Shanghai Pujiang Program(13PJ1406300)+2 种基金Natural Science Foundation of Shanghai City(13ZR1428500)Innovation Program of Shanghai Municipal Education Commission(14YZ083)Hujiang Foundation of China(C14002,B1402/D1402)
文摘Linear Least Square (LLS) is an approach for modeling regression analysis, applied for prediction and quantification of the strength of relationship between dependent and independent variables. There are a number of methods for solving the LLS problem but as soon as the data size increases and system becomes ill conditioned, the classical methods become complex at time and space with decreasing level of accuracy. Proposed work is based on prediction and quantification of the strength of relationship between sugar fasting and Post-Prandial (PP) sugar with 73 factors that affect diabetes. Due to the large number of independent variables, presented problem of diabetes prediction also presented similar complexities. ABS method is an approach proven better than other classical approaches for LLS problems. ABS algorithm has been applied for solving LLS problem. Hence, separate regression equations were obtained for sugar fasting and PP severity.
文摘This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations.The present methodcuts down computing time enormously and greatly, promotes the efficiency of the elasto-plastic andlysis for large scale structures.
基金Supported by National Natural Science Foundation of China (No.10871144)the Seed Foundation of Tianjin University (No.60302023)
文摘As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.
文摘This paper presents a condensed method for linear complementary equations of elasto-plastic problems derived from the variational inequations The present method cuts down computing time enormously and greatly promotes the efficiency of the elasto-plastic analvsis for large scale structures
