Two new formulaes of the main parameter βk of the conjugate gradient method are presented, which respectively can be seen as the modifications of method HS and PRP. In comparison with classic conjugate gradient metho...Two new formulaes of the main parameter βk of the conjugate gradient method are presented, which respectively can be seen as the modifications of method HS and PRP. In comparison with classic conjugate gradient methods, the new methods take both available gradient and function value information. Furthermore, their modifications are proposed. These methods are shown to be global convergent under some assumptions. Numerical results are also reported.展开更多
A PRP-type smoothing conjugate gradient method for solving large scale nonlinear complementarity problems （NCP（F）） is proposed. At each iteration, two Armijo line searches are performed, which guarantees the posit...A PRP-type smoothing conjugate gradient method for solving large scale nonlinear complementarity problems （NCP（F）） is proposed. At each iteration, two Armijo line searches are performed, which guarantees the positive property of the smoothing parameter and minimizes the merit function formed by Fischer-Burmeister function, respectively. Global convergence is studied when F：R^n→R^n is a continuously differentiable P0 ＋ R0 function. Numerical results show that the method is efficient.展开更多
基金supported by the Teaching and Research Award Program for the Outstanding Young Teachers in Higher Education Institutesof Ministry of Educationthe Natural Science Foundation of Inner Mongolia Autonomous Region (2010BS0108)SPH-IMU (Z20090135)
文摘Two new formulaes of the main parameter βk of the conjugate gradient method are presented, which respectively can be seen as the modifications of method HS and PRP. In comparison with classic conjugate gradient methods, the new methods take both available gradient and function value information. Furthermore, their modifications are proposed. These methods are shown to be global convergent under some assumptions. Numerical results are also reported.
基金supported by the Teaching and Research Award Program for the Outstanding Young Teachers in Higher Education Institutes of Ministry of Education,P.R.China.
文摘A PRP-type smoothing conjugate gradient method for solving large scale nonlinear complementarity problems （NCP（F）） is proposed. At each iteration, two Armijo line searches are performed, which guarantees the positive property of the smoothing parameter and minimizes the merit function formed by Fischer-Burmeister function, respectively. Global convergence is studied when F：R^n→R^n is a continuously differentiable P0 ＋ R0 function. Numerical results show that the method is efficient.
