Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.
Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.
Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China; School of Computer and Software, Nanjing University of Information Science & Technology, Nanjing 210044, P. R. China.
Gonglin
G
Yuan
Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China.
Xiabin
X
Duan
School of Computer and Software, Nanjing University of Information Science & Technology, Nanjing 210044, P. R. China; Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science & Technology, Nanjing 210044, P. R. China.
Wenjie
W
Liu
Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China.
Xiaoliang
X
Wang
Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China.
Zengru
Z
Cui
Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China.
Zhou
Z
Sheng
D000465:Algorithms; D008962:Models, Theoretical; D017711:Nonlinear Dynamics