As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initiall...As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.展开更多
This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on a...This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on any line search and only requires a simple step size formula to always generate a sufficient descent direction.Under certain assumptions,the proposed method is proved to possess global convergence.Finally,our method is compared with other potential methods.A large number of numerical experiments show that our method is more competitive and effective.展开更多
Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of n...Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of nonmonotone line search is used. Under mildassumptions, we prove the global convergence of the method. Some numerical results arealso presented.展开更多
In this paper, a new Wolfe-type line search and a new Armijo-type line searchare proposed, and some global convergence properties of a three-term conjugate gradient method withthe two line searches are proved.
In this article, a new descent memory gradient method without restarts is proposed for solving large scale unconstrained optimization problems. The method has the following attractive properties： 1） The search direc...In this article, a new descent memory gradient method without restarts is proposed for solving large scale unconstrained optimization problems. The method has the following attractive properties： 1） The search direction is always a sufficiently descent direction at every iteration without the line search used; 2） The search direction always satisfies the angle property, which is independent of the convexity of the objective function. Under mild conditions, the authors prove that the proposed method has global convergence, and its convergence rate is also investigated. The numerical results show that the new descent memory method is efficient for the given test problems.展开更多
基金supported by the National Natural Science Foundation of China(No.72071202)the Key Laboratory of Mathematics and Engineering Applications,Ministry of Education。
文摘As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.
基金Supported by 2023 Inner Mongolia University of Finance and Economics,General Scientific Research for Universities directly under Inner Mon‐golia,China (NCYWT23026)2024 High-quality Research Achievements Cultivation Fund Project of Inner Mongolia University of Finance and Economics,China (GZCG2479)。
文摘This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on any line search and only requires a simple step size formula to always generate a sufficient descent direction.Under certain assumptions,the proposed method is proved to possess global convergence.Finally,our method is compared with other potential methods.A large number of numerical experiments show that our method is more competitive and effective.
基金the National Natural Science Foundation of China(19801033,10171104).
文摘Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of nonmonotone line search is used. Under mildassumptions, we prove the global convergence of the method. Some numerical results arealso presented.
基金This research is supported by the National Natural Science Foundation of China(10171055).
文摘In this paper, a new Wolfe-type line search and a new Armijo-type line searchare proposed, and some global convergence properties of a three-term conjugate gradient method withthe two line searches are proved.
基金supported by the National Science Foundation of China under Grant No.70971076the Foundation of Shandong Provincial Education Department under Grant No.J10LA59
文摘In this article, a new descent memory gradient method without restarts is proposed for solving large scale unconstrained optimization problems. The method has the following attractive properties： 1） The search direction is always a sufficiently descent direction at every iteration without the line search used; 2） The search direction always satisfies the angle property, which is independent of the convexity of the objective function. Under mild conditions, the authors prove that the proposed method has global convergence, and its convergence rate is also investigated. The numerical results show that the new descent memory method is efficient for the given test problems.
