We applied the projection and contraction method to nonlinear complementarity problem (NCP). Moveover, we proposed an inexact implicit method for (NCP) and proved the convergence.
In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, furt...In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, further the rationality is given. When the underlying function is Lipschitz continuous, we acquire a projection and contraction algorithm to solve the approximation problem. In the end, the method is applied to some numerical experiments and the effectiveness of the algorithm is verified.展开更多
Recently, we have proposed an iterative projection and contraction (PC) method for a class of linear complementarity problems (LCP)([4]). The method was showed to be globally convergent, but no statement could be made...Recently, we have proposed an iterative projection and contraction (PC) method for a class of linear complementarity problems (LCP)([4]). The method was showed to be globally convergent, but no statement could be made about the rate of convergence. In this paper, we develop a modified globally linearly convergent PC method for linear complementarity problems. Both the method and the convergence proofs are very simple. The method can also be used to solve some linear variational inequalities. Several computational experiments are presented to indicate that the method is surprising good for solving some known difficult problems.展开更多
It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studie...It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.展开更多
Sparse signal recovery is a topic of considerable interest,and the literature in this field is already quite immense.Many problems that arise in sparse signal recovery can be generalized as a convex programming with l...Sparse signal recovery is a topic of considerable interest,and the literature in this field is already quite immense.Many problems that arise in sparse signal recovery can be generalized as a convex programming with linear conic constraints.In this paper,we present a new proximal point algorithm(PPA) termed as relaxed-PPA(RPPA) contraction method,for solving this common convex programming.More precisely,we first reformulate the convex programming into an equivalent variational inequality(VI),and then efficiently explore its inner structure.In each step,our method relaxes the VI-subproblem to a tractable one,which can be solved much more efficiently than the original VI.Under mild conditions,the convergence of the proposed method is proved.Experiments with l1 analysis show that RPPA is a computationally efficient algorithm and compares favorably with the recently proposed state-of-the-art algorithms.展开更多
A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower tha...A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower than that of ECP method in several order of magnitude.展开更多
This paper deals with a class of inertial gradient projection methods for solving a vari-ational inequality problem involving pseudomonotone and non-Lipschitz mappings in Hilbert spaces.The proposed algorithm incorpor...This paper deals with a class of inertial gradient projection methods for solving a vari-ational inequality problem involving pseudomonotone and non-Lipschitz mappings in Hilbert spaces.The proposed algorithm incorporates inertial techniques and the projection and contraction method.The weak convergence is proved without the condition of the Lipschitz continuity of the mappings.Meanwhile,the linear convergence of the algorithm is established under strong pseudomonotonicity and Lipschitz continuity assumptions.The main results obtained in this paper extend and improve some related works in the literature.展开更多
In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homot...In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method (HAM) is employed to obtain the expres- sions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.展开更多
The generalized successive overrelaxation (GSOR) method was presented and studied by Bai, Parlett and Wang [Numer. Math. 102(2005), pp.1-38] for solving the augmented system of linear equations, and the optimal it...The generalized successive overrelaxation (GSOR) method was presented and studied by Bai, Parlett and Wang [Numer. Math. 102(2005), pp.1-38] for solving the augmented system of linear equations, and the optimal iteration parameters and the corresponding optimal convergence factor were exactly obtained. In this paper, we further estimate the contraction and the semi-contraction factors of the GSOR method. The motivation of the study is that the convergence speed of an iteration method is actually decided by the contraction factor but not by the spectral radius in finite-step iteration computations. For the nonsingular augmented linear system, under some restrictions we obtain the contraction domain of the parameters involved, which guarantees that the contraction factor of the GSOR method is less than one. For the singular but consistent augmented linear system, we also obtain the semi-contraction domain of the parameters in a similar fashion. Finally, we use two numerical examples to verify the theoretical results and the effectiveness of the GSOR method.展开更多
This paper studies the linear convergence properties of a class of the projection and contraction methods for the affine variational inequalities, and proposes a necessary and sufficient condition under which PC-Metho...This paper studies the linear convergence properties of a class of the projection and contraction methods for the affine variational inequalities, and proposes a necessary and sufficient condition under which PC-Method has a globally linear convergence rate.展开更多
Presents a study which introduced a method for solving trust region problem in scale minimization. Review of the conjugate gradient method (CG) and the projection and contraction (PC) method; Convergence behavior of t...Presents a study which introduced a method for solving trust region problem in scale minimization. Review of the conjugate gradient method (CG) and the projection and contraction (PC) method; Convergence behavior of the PC method; Implementation of CG-PC method; Results; Conclusions.展开更多
基金Supported by the National Natural Science Foundation of China (No. 202001036)
文摘We applied the projection and contraction method to nonlinear complementarity problem (NCP). Moveover, we proposed an inexact implicit method for (NCP) and proved the convergence.
文摘In this paper, we study the p-order cone constraint stochastic variational inequality problem. We first take the sample average approximation method to deal with the expectation and gain an approximation problem, further the rationality is given. When the underlying function is Lipschitz continuous, we acquire a projection and contraction algorithm to solve the approximation problem. In the end, the method is applied to some numerical experiments and the effectiveness of the algorithm is verified.
文摘Recently, we have proposed an iterative projection and contraction (PC) method for a class of linear complementarity problems (LCP)([4]). The method was showed to be globally convergent, but no statement could be made about the rate of convergence. In this paper, we develop a modified globally linearly convergent PC method for linear complementarity problems. Both the method and the convergence proofs are very simple. The method can also be used to solve some linear variational inequalities. Several computational experiments are presented to indicate that the method is surprising good for solving some known difficult problems.
基金supported by Jiangsu Province NSF BK2008255The Cultivation Fund of the Key Scientific and Technical Innovation Project Ministry of Education of China 708044The Doctoral Fund of Ministry of Education of China 20060284001
文摘It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.
基金the National Natural Science Foundation of China(No.70901018)
文摘Sparse signal recovery is a topic of considerable interest,and the literature in this field is already quite immense.Many problems that arise in sparse signal recovery can be generalized as a convex programming with linear conic constraints.In this paper,we present a new proximal point algorithm(PPA) termed as relaxed-PPA(RPPA) contraction method,for solving this common convex programming.More precisely,we first reformulate the convex programming into an equivalent variational inequality(VI),and then efficiently explore its inner structure.In each step,our method relaxes the VI-subproblem to a tractable one,which can be solved much more efficiently than the original VI.Under mild conditions,the convergence of the proposed method is proved.Experiments with l1 analysis show that RPPA is a computationally efficient algorithm and compares favorably with the recently proposed state-of-the-art algorithms.
文摘A new branch of hypergraph theory-directed hyperaph theory and a kind of new methods-dicomposition contraction(DCP, PDCP and GDC) methods are presented for solving hypernetwork problems.lts computing time is lower than that of ECP method in several order of magnitude.
文摘This paper deals with a class of inertial gradient projection methods for solving a vari-ational inequality problem involving pseudomonotone and non-Lipschitz mappings in Hilbert spaces.The proposed algorithm incorporates inertial techniques and the projection and contraction method.The weak convergence is proved without the condition of the Lipschitz continuity of the mappings.Meanwhile,the linear convergence of the algorithm is established under strong pseudomonotonicity and Lipschitz continuity assumptions.The main results obtained in this paper extend and improve some related works in the literature.
基金supported by the National Natural Science Foundations of China (50936003, 50905013)The Open Project of State Key Lab. for Adv. Matals and Materials (2009Z-02)Research Foundation of Engineering Research Institute of USTB
文摘In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method (HAM) is employed to obtain the expres- sions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.
基金supported by State Key Laboratory of Scientific/Engineering Computing,Chinese Academy of SciencesThe National Key Basic Research Program of China (973 program) under Grant 2005CB321701+2 种基金The National Natural Science Foundation (No. 10771168)The Natural Science and Technology Development Plan Research Project of Shaanxi Province (No. 2008K01-33)The Special Plan Research Project of Shaanxi Education Department (No. 09JK716),P.R.China
文摘The generalized successive overrelaxation (GSOR) method was presented and studied by Bai, Parlett and Wang [Numer. Math. 102(2005), pp.1-38] for solving the augmented system of linear equations, and the optimal iteration parameters and the corresponding optimal convergence factor were exactly obtained. In this paper, we further estimate the contraction and the semi-contraction factors of the GSOR method. The motivation of the study is that the convergence speed of an iteration method is actually decided by the contraction factor but not by the spectral radius in finite-step iteration computations. For the nonsingular augmented linear system, under some restrictions we obtain the contraction domain of the parameters involved, which guarantees that the contraction factor of the GSOR method is less than one. For the singular but consistent augmented linear system, we also obtain the semi-contraction domain of the parameters in a similar fashion. Finally, we use two numerical examples to verify the theoretical results and the effectiveness of the GSOR method.
文摘This paper studies the linear convergence properties of a class of the projection and contraction methods for the affine variational inequalities, and proposes a necessary and sufficient condition under which PC-Method has a globally linear convergence rate.
文摘Presents a study which introduced a method for solving trust region problem in scale minimization. Review of the conjugate gradient method (CG) and the projection and contraction (PC) method; Convergence behavior of the PC method; Implementation of CG-PC method; Results; Conclusions.