In this paper,an adaptive three-term conjugate gradient method is proposed for solving unconstrained problems,which generates sufficient descent directions at each iteration.Different from the existent methods,a dynam...In this paper,an adaptive three-term conjugate gradient method is proposed for solving unconstrained problems,which generates sufficient descent directions at each iteration.Different from the existent methods,a dynamical adjustment between Hestenes–Stiefel and Dai–Liao conjugacy conditions in our proposed method is developed.Under mild condition,we show that the proposed method converges globally.Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising.展开更多
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
基金This work was supported by First-Class Disciplines Foundation of Ningxia Hui Autonomous Region(No.NXYLXK2017B09)the National Natural Science Foundation of China(Nos.11601012,11861002,71771030)+3 种基金the Key Project of North Minzu University(No.ZDZX201804)Natural Science Foundation of Ningxia Hui Autonomous Region(Nos.NZ17103,2018AAC03253)Natural Science Foundation of Guangxi Zhuang Autonomous Region(No.2018GXNSFAA138169)Guangxi Key Laboratory of Cryptography and Information Security(No.GCIS201708).
文摘In this paper,an adaptive three-term conjugate gradient method is proposed for solving unconstrained problems,which generates sufficient descent directions at each iteration.Different from the existent methods,a dynamical adjustment between Hestenes–Stiefel and Dai–Liao conjugacy conditions in our proposed method is developed.Under mild condition,we show that the proposed method converges globally.Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising.
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.
