In this paper,a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong(Appl.Math.Lett.1...In this paper,a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong(Appl.Math.Lett.134:108344,2022).The convergence analysis of the proposed method is established,which can improve the existing results.Numerical examples show that the proposed method is efficient with the two-step technique.展开更多
For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matr...For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.展开更多
In this paper,by means of constructing the linear complementarity problems into the corresponding absolute value equation,we raise an iteration method,called as the nonlinear lopsided HSS-like modulus-based matrix spl...In this paper,by means of constructing the linear complementarity problems into the corresponding absolute value equation,we raise an iteration method,called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method,for solving the linear complementarity problems whose coefficient matrix in R^(n×n)is large sparse and positive definite.From the convergence analysis,it is appreciable to see that the proposed method will converge to its accurate solution under appropriate conditions.Numerical examples demonstrate that the presented method precede to other methods in practical implementation.展开更多
In this paper,we present a modulus-based multisplitting iteration method based on multisplitting of the system matrix for a class of weakly nonlinear complementarity problem.And we prove the convergence of the method ...In this paper,we present a modulus-based multisplitting iteration method based on multisplitting of the system matrix for a class of weakly nonlinear complementarity problem.And we prove the convergence of the method when the system matrix is an H_(+)-matrix.Finally,we give two numerical examples.展开更多
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent im...In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.展开更多
We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterativ...We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterative method is adopted as a smoother,which can accelerate the convergence of the new methods.We also give the convergence analysis of these methods.Finally,some numerical experiments confirm the theoretical analysis and show that the new methods can achieve high efficiency and lower costs simultaneously.展开更多
The mathematical formulation of the mixed-cell-height circuit legalization(MCHCL)problem can be expressed by a linear complementarity problem(LCP)with the system matrix being a block two-by-two saddle point matrix.Bas...The mathematical formulation of the mixed-cell-height circuit legalization(MCHCL)problem can be expressed by a linear complementarity problem(LCP)with the system matrix being a block two-by-two saddle point matrix.Based on the robust modulus-based matrix splitting(RMMS)iteration method and its two-step improvement(RTMMS)studied recently,the well-known Hermitian and skew-Hermitian splitting iteration method and the generalized successive overrelaxation iteration method for solving saddle point linear systems,two variants of robust two-step modulus-based matrix splitting(VRTMMS)iteration methods are proposed for solving the MCHCL problem.Convergence analyses of the proposed two iteration methods are studied in detail.Finally,five test problems are presented.Numerical results show that the proposed two VRTMMS iteration methods not only take full use of the sparse property of the circuit system but also speed up the computational efficiency of the existing RMMS and RTMMS iteration methods for solving the MCHCL problem.展开更多
In this paper,the modulus-based matrix splitting(MMS)iteration method is extended to solve the horizontal quasi-complementarity problem(HQCP),which is characterized by the presence of two system matrices and two nonli...In this paper,the modulus-based matrix splitting(MMS)iteration method is extended to solve the horizontal quasi-complementarity problem(HQCP),which is characterized by the presence of two system matrices and two nonlinear functions.Based on the specific matrix splitting of the system matrices,a series of MMS relaxation iteration methods are presented.Convergence analyses of the MMS iteration method are carefully studied when the system matrices are positive definite matrices and H_(+)-matrices,respectively.Finally,two numerical examples are given to illustrate the efficiency of the proposed MMS iteration methods.展开更多
To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based syn- chronous multisplitting iteration method and the corres...To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based syn- chronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an H＋-matrix, which improve the existing convergence theory. Numeri- cal results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation.展开更多
Our goal is to improve the convergence theory of the one-step modulus-based synchronous multisplitting(MSM)and the two-step modulus-based synchronous multisplitting(TMSM)iteration methods for a class of nondifferentia...Our goal is to improve the convergence theory of the one-step modulus-based synchronous multisplitting(MSM)and the two-step modulus-based synchronous multisplitting(TMSM)iteration methods for a class of nondifferentiable nonlinear complementarity problems(NCPs)with H_(+)-matrices.The analysis is developed and the results are renewed under some conditions weakened than before.展开更多
基金supported by the Scientific Computing Research Innovation Team of Guangdong Province(no.2021KCXTD052)the Science and Technology Development Fund,Macao SAR(no.0096/2022/A,0151/2022/A)+3 种基金University of Macao(no.MYRG2020-00035-FST,MYRG2022-00076-FST)the Guangdong Key Construction Discipline Research Capacity Enhancement Project(no.2022ZDJS049)Technology Planning Project of Shaoguan(no.210716094530390)the ScienceFoundation of Shaoguan University(no.SZ2020KJ01).
文摘In this paper,a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong(Appl.Math.Lett.134:108344,2022).The convergence analysis of the proposed method is established,which can improve the existing results.Numerical examples show that the proposed method is efficient with the two-step technique.
文摘For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.
基金This work is supported by the National Natural Science Foundation of China with No.11461046the Natural Science Foundation of Jiangxi Province of China with Nos.20181ACB20001 and 20161ACB21005.
文摘In this paper,by means of constructing the linear complementarity problems into the corresponding absolute value equation,we raise an iteration method,called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method,for solving the linear complementarity problems whose coefficient matrix in R^(n×n)is large sparse and positive definite.From the convergence analysis,it is appreciable to see that the proposed method will converge to its accurate solution under appropriate conditions.Numerical examples demonstrate that the presented method precede to other methods in practical implementation.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11771275)the Science and Technology Program of Shandong Universities(No.J16LI04).
文摘In this paper,we present a modulus-based multisplitting iteration method based on multisplitting of the system matrix for a class of weakly nonlinear complementarity problem.And we prove the convergence of the method when the system matrix is an H_(+)-matrix.Finally,we give two numerical examples.
文摘In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.
基金National Natural Science Foundation of China(12161027)Guangxi Natural Science Foundation,China(2020GXNSFAA159143)Science and Technology Project of Guangxi,China(AD23023002).
文摘We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterative method is adopted as a smoother,which can accelerate the convergence of the new methods.We also give the convergence analysis of these methods.Finally,some numerical experiments confirm the theoretical analysis and show that the new methods can achieve high efficiency and lower costs simultaneously.
基金National Natural Science Foundation of China(No.11771225)the Qinglan Project of Jiangsu Province and the Science and Technology Project of Nantong City of China(No.JC2021198).
文摘The mathematical formulation of the mixed-cell-height circuit legalization(MCHCL)problem can be expressed by a linear complementarity problem(LCP)with the system matrix being a block two-by-two saddle point matrix.Based on the robust modulus-based matrix splitting(RMMS)iteration method and its two-step improvement(RTMMS)studied recently,the well-known Hermitian and skew-Hermitian splitting iteration method and the generalized successive overrelaxation iteration method for solving saddle point linear systems,two variants of robust two-step modulus-based matrix splitting(VRTMMS)iteration methods are proposed for solving the MCHCL problem.Convergence analyses of the proposed two iteration methods are studied in detail.Finally,five test problems are presented.Numerical results show that the proposed two VRTMMS iteration methods not only take full use of the sparse property of the circuit system but also speed up the computational efficiency of the existing RMMS and RTMMS iteration methods for solving the MCHCL problem.
基金supported by the National Natural Science Foundation of China(No.11771225)the Qinglan Project of Jiangsu Province of Chinathe Science and Technology Project of Nantong City of China(No.JC2021198).
文摘In this paper,the modulus-based matrix splitting(MMS)iteration method is extended to solve the horizontal quasi-complementarity problem(HQCP),which is characterized by the presence of two system matrices and two nonlinear functions.Based on the specific matrix splitting of the system matrices,a series of MMS relaxation iteration methods are presented.Convergence analyses of the MMS iteration method are carefully studied when the system matrices are positive definite matrices and H_(+)-matrices,respectively.Finally,two numerical examples are given to illustrate the efficiency of the proposed MMS iteration methods.
文摘To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based syn- chronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an H＋-matrix, which improve the existing convergence theory. Numeri- cal results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation.
基金supported by the National Natural Science Foundation of China with Grant Nos.12161030 and 12261073。
文摘Our goal is to improve the convergence theory of the one-step modulus-based synchronous multisplitting(MSM)and the two-step modulus-based synchronous multisplitting(TMSM)iteration methods for a class of nondifferentiable nonlinear complementarity problems(NCPs)with H_(+)-matrices.The analysis is developed and the results are renewed under some conditions weakened than before.
