| 优化问题的新步长法则 |
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| 引用本文： | 吴庆军,韦增欣. 优化问题的新步长法则[J]. 上海大学学报(英文版), 2007, 11(2): 135-141. DOI: 10.1007/s11741-007-0209-8 |
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| 作者姓名： | 吴庆军 韦增欣 |
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| 作者单位： | Department of Mathematics and Computer Science Yulin Teacher's College，College of Mathematics and Information Science，Guangxi University，Yulin 537000，P.R.China，Nanning 530004，P.R.China |
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| 基金项目： | 国家自然科学基金;广西自然科学基金 |
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| 摘 要： | The step-size procedure is very important for solving optimization problems. The Armijo step-size rule, the Armijo-Goldstein step-size rule and the Wolfe-Powell step-size rule are three well-known line search methods. On the basis of the above three types of line search methods and the idea of the proximal point methods, a new class of step-size rules was proposed. Instead of a single objective function f, f ＋1/2（x - xk）^TBk（x-Xk） was used as the merit function in iteration k, where Sk is a given symmetric positive definite matrix. The existence of the steplength for the new rules was proved. Some convergence properties were also discussed.
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| 关 键 词： | 步长搜索准则 优化问题 未约束最小化 全局收敛 |
| 收稿时间： | 2005-03-30 |
| 修稿时间： | 2005-05-09 |
Some new step-size rules for optimization problems |
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| Wu Qing-jun,Wei Zeng-xin. Some new step-size rules for optimization problems[J]. Journal of Shanghai University(English Edition), 2007, 11(2): 135-141. DOI: 10.1007/s11741-007-0209-8 |
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| Authors: | Wu Qing-jun Wei Zeng-xin |
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| Affiliation: | 1. Department of Mathematics and Computer Science, Yulin Teacher's College, Yulin 537000, P. R. China
2. College of Mathematics and Information Science, Guangxi University, Nanning 530004, P. R. China |
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| Abstract: | The step-size procedure is very important for solving optimization problems.The Armijo step-size rule,the Armijo-Goldstein step-size rule and the Wolfe-Powell step-size rule are three well-known line search methods.On the basis of the above three types of line search methods and the idea of the proximal point methods,a new class of step-size rules was proposed.Instead of a single objective function f,f 1/2(x-x_k)~TB_k(x-x_k)was used as the merit function in iteration k, where B_k is a given symmetric positive definite matrix.The existence of the steplength for the new rules was proved.Some convergence properties were also discussed. |
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| Keywords: | unconstrained minimization step-size procedures global convergence |
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