| 结合修正Curry-Altman步长搜索一个新的共轭梯度算法的收敛性 |
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| 引用本文： | CAO Li-hua,SUN Qing-ying(Department of Mathematics,Shenzhen University,Shenzhen 518060,China, Department of Applied Mathematics,University of Petroleum,Dongying 257062,China ). 结合修正Curry-Altman步长搜索一个新的共轭梯度算法的收敛性[J]. 数学季刊, 2004, 19(2): 198-204 |
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| 作者姓名： | CAO Li-hua SUN Qing-ying(Department of Mathematics Shenzhen University Shenzhen 518060 China Department of Applied Mathematics University of Petroleum Dongying 257062 China ) |
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| 作者单位： | Department of Mathematics，Shenzhen University，Shenzhen 518060，China; Department of Applied Mathematics，University of Petroleum，Dongying 257062，China |
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| 摘 要： | Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman‘s step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property.Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method.
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| 关 键 词： | 非线性规划 最优化 运算法则 函数 |
Global Convergence of a New Conjugate Gradient Methods with a Modification of the Curry-Altman Step-size Rule |
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| CAOLi-hua SUNQing-ying. Global Convergence of a New Conjugate Gradient Methods with a Modification of the Curry-Altman Step-size Rule[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(2): 198-204 |
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| Authors: | CAOLi-hua SUNQing-ying |
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| Affiliation: | [1]DepartmentofMathematics,ShenzhenUniversity,Shenzhen518060,China [2]DepartmentofAppliedMathematics,UniversityofPetroleum,Dongying257062,China |
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| Abstract: | Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman's step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property. Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method. |
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| Keywords: | nonlinear programming forcing function reverse modulus of continuity function convergence |
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