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, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required...In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration, thus avoiding the need for solving a quadratic subproblem with a trust region bound. Under some conditions, it is proven that this algorithm is globally and locally superlinear convergent. The limited numerical examples show its efficiency.展开更多
In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution c...In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution curve. The numerical tests confirm the efficiency of our proposed method.展开更多
In this paper, we present a new form of successive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we get the global c...In this paper, we present a new form of successive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we get the global convergence on the algorithms. Some numerical results are also reported.展开更多
Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Ou...Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.展开更多
A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theore...A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition,some numerical results are reported.展开更多
A class of strongly nonlinear implicit complementarity problems for set-valued mappings in Hilbert spaces is studied,Thereupon a new existence theorem is established and proved to be a solution to that kind of problems.
In this paper, we propose an inexact damped Newtonmethod for solving nonlinear complementarity problems based on the equivalent B differentiable equations.Global convergence and locally quadratic convergence are ...In this paper, we propose an inexact damped Newtonmethod for solving nonlinear complementarity problems based on the equivalent B differentiable equations.Global convergence and locally quadratic convergence are obtained,and numerical results are given.展开更多
A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization pro...A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.展开更多
By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by...By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption.展开更多
In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinea...In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinear operator from K into E* (i. e.,the dual space of E) and S is a nonlinear operator from K into E. Our results are the essential improvements and extension of the results obtained previously by several authors including Thera,Ding,and Zeng.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, based on the resuls presented in part I of this paper[18],we present a numerical crabeding algorithm for soling the nonlinear complementarity problem, and prove its convergence carefully. Numerical expe...In this paper, based on the resuls presented in part I of this paper[18],we present a numerical crabeding algorithm for soling the nonlinear complementarity problem, and prove its convergence carefully. Numerical experiments show that the algorithm is successful.展开更多
In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is ...In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is presented.It is shown that the algorithm is globally and locally superlinearly (quadratically) convergent without the assumption of monotonicity.展开更多
The existence condition of the solution of special nonlinear penalized equation of the linear complementarity problems is obtained by the relationship between penalized equations and an absolute value equation. Newton...The existence condition of the solution of special nonlinear penalized equation of the linear complementarity problems is obtained by the relationship between penalized equations and an absolute value equation. Newton method is used to solve penalized equation, and then the solution of the linear complementarity problems is obtained. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems of its singular values exceeds 0;numerical results show that our proposed method is very effective and efficient.展开更多
In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the...In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the problem. The resulting problems are nonlinear programs that can be solved by a line search filter-SQP algorithm.展开更多
The penalty equation of LCP is transformed into the absolute value equation, and then the existence of solutions for the penalty equation is proved by the regularity of the interval matrix. We propose a generalized Ne...The penalty equation of LCP is transformed into the absolute value equation, and then the existence of solutions for the penalty equation is proved by the regularity of the interval matrix. We propose a generalized Newton method for solving the linear complementarity problem with the regular interval matrix based on the nonlinear penalized equation. Further, we prove that this method is convergent. Numerical experiments are presented to show that the generalized Newton method is effective.展开更多
This paper considers semidefinite relaxation for linear and nonlinear complementarity problems.For some particular copositive matrices and tensors,the existence of a solution for the corresponding complementarity prob...This paper considers semidefinite relaxation for linear and nonlinear complementarity problems.For some particular copositive matrices and tensors,the existence of a solution for the corresponding complementarity problems is studied.Under a general assumption,we show that if the solution set of a complementarity problem is nonempty,then we can get a solution by the semidefinite relaxation method;while if it does not have a solution,we can obtain a certificate for the infeasibility.Some numerical examples are given.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
In this paper, we present a new successive approximation damped Newton method for the nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we obtain the global conv...In this paper, we present a new successive approximation damped Newton method for the nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we obtain the global convergence result of the proposed algorithms. Some numerical results are also reported.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.
基金Supported by the Natural Science Foundation of Hainan Province(80552)
文摘In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration, thus avoiding the need for solving a quadratic subproblem with a trust region bound. Under some conditions, it is proven that this algorithm is globally and locally superlinear convergent. The limited numerical examples show its efficiency.
文摘In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution curve. The numerical tests confirm the efficiency of our proposed method.
文摘In this paper, we present a new form of successive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we get the global convergence on the algorithms. Some numerical results are also reported.
文摘Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.
文摘A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition,some numerical results are reported.
文摘A class of strongly nonlinear implicit complementarity problems for set-valued mappings in Hilbert spaces is studied,Thereupon a new existence theorem is established and proved to be a solution to that kind of problems.
文摘In this paper, we propose an inexact damped Newtonmethod for solving nonlinear complementarity problems based on the equivalent B differentiable equations.Global convergence and locally quadratic convergence are obtained,and numerical results are given.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10571137,10771162)
文摘A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.
基金Supported by China Postdoctoral Science Foundation(No.20060390660)Science and Technology Development Plan of Tianjin(No.06YFGZGX05600)+1 种基金Scientific Research Foundation of Liu Hui Center for Applied MathematicsNankai University-Tianjin University.
文摘By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption.
文摘In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinear operator from K into E* (i. e.,the dual space of E) and S is a nonlinear operator from K into E. Our results are the essential improvements and extension of the results obtained previously by several authors including Thera,Ding,and Zeng.
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.
基金Supported by the National Natural Science Foundation of China and Development Foundation of Shanghai Universities
文摘In this paper, based on the resuls presented in part I of this paper[18],we present a numerical crabeding algorithm for soling the nonlinear complementarity problem, and prove its convergence carefully. Numerical experiments show that the algorithm is successful.
基金Supported by the National Natural Science Foundation of China(1 9971 0 0 2 )
文摘In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is presented.It is shown that the algorithm is globally and locally superlinearly (quadratically) convergent without the assumption of monotonicity.
文摘The existence condition of the solution of special nonlinear penalized equation of the linear complementarity problems is obtained by the relationship between penalized equations and an absolute value equation. Newton method is used to solve penalized equation, and then the solution of the linear complementarity problems is obtained. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems of its singular values exceeds 0;numerical results show that our proposed method is very effective and efficient.
文摘In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the problem. The resulting problems are nonlinear programs that can be solved by a line search filter-SQP algorithm.
文摘The penalty equation of LCP is transformed into the absolute value equation, and then the existence of solutions for the penalty equation is proved by the regularity of the interval matrix. We propose a generalized Newton method for solving the linear complementarity problem with the regular interval matrix based on the nonlinear penalized equation. Further, we prove that this method is convergent. Numerical experiments are presented to show that the generalized Newton method is effective.
基金supported by the National Natural Science Foundation of China(Nos.12171105,11271206)the Fundamental Research Funds for the Central Universities(No.FRF-DF-19-004).
文摘This paper considers semidefinite relaxation for linear and nonlinear complementarity problems.For some particular copositive matrices and tensors,the existence of a solution for the corresponding complementarity problems is studied.Under a general assumption,we show that if the solution set of a complementarity problem is nonempty,then we can get a solution by the semidefinite relaxation method;while if it does not have a solution,we can obtain a certificate for the infeasibility.Some numerical examples are given.
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.
文摘In this paper, we present a new successive approximation damped Newton method for the nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we obtain the global convergence result of the proposed algorithms. Some numerical results are also reported.
