Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology ...Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.展开更多
In this paper,we construct a new algorithm which combines the conjugate gradient and Lanczos methods for solving nonlinear systems.The iterative direction can be obtained by solving a quadratic model via conjugate gra...In this paper,we construct a new algorithm which combines the conjugate gradient and Lanczos methods for solving nonlinear systems.The iterative direction can be obtained by solving a quadratic model via conjugate gradient and Lanczos methods.Using the backtracking line search,we will find an acceptable trial step size along this direction which makes the objective function nonmonotonically decreasing and makes the norm of the step size monotonically increasing.Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions.Finally,we present some numerical results to illustrate the effectiveness of the proposed algorithm.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant No.11901561).
文摘Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.
基金supports of the National Natural Science Foundation of China(No.11371253).
文摘In this paper,we construct a new algorithm which combines the conjugate gradient and Lanczos methods for solving nonlinear systems.The iterative direction can be obtained by solving a quadratic model via conjugate gradient and Lanczos methods.Using the backtracking line search,we will find an acceptable trial step size along this direction which makes the objective function nonmonotonically decreasing and makes the norm of the step size monotonically increasing.Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions.Finally,we present some numerical results to illustrate the effectiveness of the proposed algorithm.
基金The National Natural Science Foundation of China(6097301561170311)+2 种基金the Specialized Research Fund for the Doctoral Program in China Universities(20110185110020)the Science & Technology Research Project of Sichuan Province(2009SPT-112ZC1802)
