By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities （BVIs） was constructed. The function is simple and has some good differential ...By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities （BVIs） was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it. Global and local superlinear/ quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.展开更多
Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generMized Fischer-Burmeister function, a smoothing trust re- gion Mgorithm with line search is proposed for solv...Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generMized Fischer-Burmeister function, a smoothing trust re- gion Mgorithm with line search is proposed for solving general （not necessarily monotone） nonlinear complementarity problems. Global convergence and, under a nonsingularity assumption, local Q-superlinear/Q-quadratic convergence of the algorithm are established. In particular, it is proved that a unit step size is always accepted after a finite number of iterations. Numerical results also confirm the good theoretical properties of our approach.展开更多
In this paper,we propose a regularized version of the generalized NCPfunction proposed by Hu,Huang and Chen[J.Comput.Appl.Math.,230(2009),pp.69–82].Based on this regularized function,we propose a semismooth Newton me...In this paper,we propose a regularized version of the generalized NCPfunction proposed by Hu,Huang and Chen[J.Comput.Appl.Math.,230(2009),pp.69–82].Based on this regularized function,we propose a semismooth Newton method for solving nonlinear complementarity problems,where a non-monotone line search scheme is used.In particular,we show that the proposed non-monotone method is globally and locally superlinearly convergent under suitable assumptions.We test the proposed method by solving the test problems from MCPLIB.Numerical experiments indicate that this algorithm has better numerical performance in the case of p=5 andθ∈[0.25,075]than other cases.展开更多
文摘By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities （BVIs） was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it. Global and local superlinear/ quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.
基金Acknowledgments. The work was supported by the National Natural Science Foundation of China （11071041） and Fujian Natural Science Foundation （2009J01002）.
文摘Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generMized Fischer-Burmeister function, a smoothing trust re- gion Mgorithm with line search is proposed for solving general （not necessarily monotone） nonlinear complementarity problems. Global convergence and, under a nonsingularity assumption, local Q-superlinear/Q-quadratic convergence of the algorithm are established. In particular, it is proved that a unit step size is always accepted after a finite number of iterations. Numerical results also confirm the good theoretical properties of our approach.
文摘In this paper,we propose a regularized version of the generalized NCPfunction proposed by Hu,Huang and Chen[J.Comput.Appl.Math.,230(2009),pp.69–82].Based on this regularized function,we propose a semismooth Newton method for solving nonlinear complementarity problems,where a non-monotone line search scheme is used.In particular,we show that the proposed non-monotone method is globally and locally superlinearly convergent under suitable assumptions.We test the proposed method by solving the test problems from MCPLIB.Numerical experiments indicate that this algorithm has better numerical performance in the case of p=5 andθ∈[0.25,075]than other cases.
