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一类带非单调线搜索的信赖域算法
A NEW FAMILY OF TRUST REGION ALGORITHMS WITH A NONMONOTONE LINE SEARCH TECHNIQUE
查看参考文献13篇
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文摘
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通过将非单调Wolfe线搜索技术与传统的信赖域算法相结合, 我们提出了一类新的求解无约束最优化问题的信赖域算法, 新算法在每一迭代步只需求解一次信赖域子问题, 而且在每一迭代步Hesse阵的近似都满足拟牛顿条件并保持正定传递.在一定条件下, 证明了算法的全局收敛性和强收敛性, 数值试验表明新算法继承了非单调技术的优点, 对于求解某些优化问题具有重要意义 |
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其他语种文摘
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We propose a new family of trust region algorithms for unconstrained optimization problems which is combining traditional trust region method with a nonmonotone Wolfe line search technique. The new algorithm solves the trust region subproblem only once at each iteration, furthermore, the matrix approximation to the Hessian simultaneously satisfies the quasi-Newton condition at each iteration and maintains its positive definiteness. Under certain conditions, the global convergence and strong global convergence of the algorithm are proved. Numerical results show that the algorithm inherits the advantages of the nonmonotone schemes and is meaningful to some optimization problems |
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来源
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计算数学
,2011,33(1):48-56 【核心库】
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关键词
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无约束最优化
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信赖域方法
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非单调线搜索
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全局收敛
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地址
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首都师范大学数学科学学院, 北京, 100048
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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0254-7791 |
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学科
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数学 |
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基金
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国家自然科学基金
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文献收藏号
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CSCD:4144321
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参考文献 共
13
共1页
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1.
刘培培. 一类拟牛顿非单调信赖域算法及其收敛性.
数学进展,2008,37(1):92-100
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被引
6
次
|
|
|
|
|
2.
Michael Gertz E.
Combination trust-region line search methods for unconstrained optimization,1999
|
被引
1
次
|
|
|
|
|
3.
Nocedal J.
Combining trust region and line search techniques. Technical Report, NAM06,1991
|
被引
1
次
|
|
|
|
|
4.
Nocedal J. Combining Trust Region and Line Search Techniques.
Advances in Nonlinear Programming,1998:153-175
|
被引
25
次
|
|
|
|
|
5.
袁亚湘.
最优化理论与方法,1997:154-166
|
被引
8
次
|
|
|
|
|
6.
Michael Gertz E. A quasi-Newton trust-region method.
Mathematical Programming,2004,100(3):447-470
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被引
9
次
|
|
|
|
|
7.
Grippo L. A global convergence version of the Plak-Ribiere conjugate gradient method.
Mathematical Programming,1997,78:375-391
|
被引
29
次
|
|
|
|
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8.
Grippo L. A nonmonotone line search technique for Newton's method.
SIAM J. Numer. Anal,1986,23(4):707-716
|
被引
115
次
|
|
|
|
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9.
Zhang H C. A nonmonotone line search technique and its application to unconstrained optimization.
SIAM J. Optim,2004,14(4):1043-1056
|
被引
45
次
|
|
|
|
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10.
席少霖.
非线性最优化方法,1992:102-112
|
被引
2
次
|
|
|
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11.
Deng N Y. A nonmonotonic trust region algorithm.
Journal of optimization Theory and Applications,1993,76(2):259-285
|
被引
57
次
|
|
|
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12.
Jorge J More. Testing Unconstrained Optimization Software.
ACM Transactions on Mathematical Software,1981,7(1):17-41
|
被引
143
次
|
|
|
|
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13.
柯小伍. 一类新的信赖域算法的全局收敛性.
应用数学学报,1995,18(4):608-615
|
被引
14
次
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