The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing...The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.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
The system of generalized absolute value equations(GAVE)has attracted more and more attention in the optimization community.In this paper,by introducing a smoothing function,we develop a smoothing Newton algorithm wit...The system of generalized absolute value equations(GAVE)has attracted more and more attention in the optimization community.In this paper,by introducing a smoothing function,we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE.We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE.Numerical results are given to demonstrate the viability and efficiency of the approach.展开更多
基金Supported by LIU Hui Centre for Applied Mathematics of Nankai University and Tianjin University
文摘The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.
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.
基金supported by the Natural Science Foundation of Fujian Province(Grant No.2021J01661)by the National Natural Science Foundation of China(Grant No.11901024)+5 种基金supported by the National Natural Science Foundation of China(Grant No.12201275)by the Ministry of Education in China of Humanities and Social Science Project(Grant No.21YJCZH204)by the Liaoning Provincial Department of Education(Grant No.JYTZD2023072)supported by the National Natural Science Foundation of China(Grant No.12131004)by the Ministry of Science and Technology of China(Grant No.2021YFA1003600)supported by the National Key Research and Development Program of China(Grant No.2019YFC0312003).
文摘The system of generalized absolute value equations(GAVE)has attracted more and more attention in the optimization community.In this paper,by introducing a smoothing function,we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE.We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE.Numerical results are given to demonstrate the viability and efficiency of the approach.
