| 求解无约束非线性规划问题的一个新的重开始共轭梯度算法的收敛性 |
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| 引用本文： | 孙清滢.求解无约束非线性规划问题的一个新的重开始共轭梯度算法的收敛性[J].数学季刊,2003,18(2):154-162. |
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| 作者姓名： | 孙清滢 |
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| 作者单位： | Department of Applied Mathematics，Dalian University of Technology，Dalian 116024，China; Department of Applied Mathematics，University of Petroleum，Dongying 257061，China |
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| 摘 要： | Conjugate gradient optimization algorithms depend on the search directions.with different choices for the parameters in the search directions.In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991),a class of new restarting conjugate gradient methods is presented.Global convergences of the new method with two kinds of common line searches,are proved .Firstly,it is shown that,using reverse modulus of continuity funciton and forcing function,the new method for solving unconstrained optimization can work for a continously differentiable function with Curry-Altman‘s step size rule and a bounded level set .Secondly,by using comparing technique,some general convergence propecties of the new method with other kind of step size rule are established,Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.
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| 关 键 词： | 全局收敛性 重开始共轭梯度算法 无约束非线性规划 强制函数 逆模 线性搜索 FR方法 HS方法 Curry－Altman步长法则 |
Global Convergence of a New Restarting Conjugate Gradient Method for Nonlinear Optimizations |
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| SUNQing-ying.Global Convergence of a New Restarting Conjugate Gradient Method for Nonlinear Optimizations[J].Chinese Quarterly Journal of Mathematics,2003,18(2):154-162. |
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| Authors: | SUNQing-ying |
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| Institution: | DepartmentofAppliedMathematics,DalianUniversityofTechnology,Dalian116024,China;DepartmentofAppliedMathematics,UniversityofPetroleum.Dongying257061,China |
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| Abstract: | Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method. |
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| Keywords: | nonlinear programming restarting conjugate gradient method forcing function reverse modulus of continuity function convergence |
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