| On the use of simplex methods in constructing quadratic models |
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| 作者姓名： | Qing-hua ZHOU College of Mathematics and Computer Hebei University Baoding China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China |
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| 作者单位： | Qing-hua ZHOU 1 College of Mathematics and Computer，Hebei University，Baoding 071002，China; 2 State Key Laboratory of Scientific and Engineering Computing，Institute of Computational Mathematics and Scientific/Engineering Computing，Academy of Mathematics and Systems Science，Chinese Academy of Sciences，Beijing 100080，China |
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| 基金项目： | 河北大学校科研和教改项目;国家自然科学基金 |
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| 摘 要： | In this paper,we investigate the quadratic approximation methods.After studying the basic idea of simplex methods,we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces.And the quadratic model is solved in the new subspaces.The motivation is to use the information disclosed by the former steps to construct more promising directions.For most tested problems,the number of function evaluations have been reduced obviously through our algorithms.
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| 收稿时间： | 7 June 2006 |
| 修稿时间： | 19 January 2007 |
On the use of simplex methods in constructing quadratic models |
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| Qing-hua ZHOU College of Mathematics and Computer,Hebei University,Baoding ,China, State Key Laboratory of Scientific and Engineering Computing,Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing ,China.On the use of simplex methods in constructing quadratic models[J].Science in China(Mathematics),2007,50(7):913-924. |
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| Authors: | Qing-hua Zhou |
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| Institution: | College of Mathematics and Computer, Hebei University,Baoding 071002,China;State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | In this paper,we investigate the quadratic approximation methods.After studying the basic idea of simplex methods,we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces.And the quadratic model is solved in the new subspaces.The motivation is to use the information disclosed by the former steps to construct more promising directions.For most tested problems,the number of function evaluations have been reduced obviously through our algorithms. |
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| Keywords: | unconstrained optimization trust region method quadratic model Lagrange function simplex methods direct methods |
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