| 采用不定Dogleg路径的非单调自适应信赖域算法解无约束极小化(英文) |
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| 引用本文： | 陈俊,孙文瑜.采用不定Dogleg路径的非单调自适应信赖域算法解无约束极小化(英文)[J].东北数学,2008,24(1):19-30. |
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| 作者姓名： | 陈俊 孙文瑜 |
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| 作者单位： | School of Mathematics and Computer Science;Nanjing Normal University;Department of Mathematics;Nanjing Xiaozhuang Colleage; |
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| 基金项目： | 国家自然科学基金
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教育部高等学校博士学科点专项科研基金
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江苏省自然科学基金
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南京晓庄学院科学基金 |
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| 摘 要： | In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the monotone sequence, the nonmonotone sequence of function values are employed. With the adaptive technique, the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods. By means of the Bunch-Parlett factorization, we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk. The convergence properties of the algorithm are established. Finally, detailed numerical results are reported to show that our algorithm is efficient.
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| 关 键 词： | 不定Dogleg路径 非单调自适应信赖域算法 解法 无约束极小化 |
Nonmonotone Adaptive Trust Region Algorithms with Indefinite Dogleg Path for Unconstrained Minimization |
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| CHEN JunSUN Wen-yu.Nonmonotone Adaptive Trust Region Algorithms with Indefinite Dogleg Path for Unconstrained Minimization[J].Northeastern Mathematical Journal,2008,24(1):19-30. |
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| Authors: | CHEN JunSUN Wen-yu |
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| Institution: | [1]School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, 210097 [2]Department of Mathematics, Nanjing Xiaozhuang Colleage, Nanjing, 210017 |
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| Abstract: | In this paper,we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems.We set a new ratio of the actual descent and predicted descent.Then,instead of the monotone sequence,the nonmonotone sequence of function values are employed.With the adaptive technique,the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods.By means of the Bunch-Parlett factorization,we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk.The convergence properties of the algorithm are established.Finally,detailed numerical results are reported to show that our algorithm is efficient. |
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| Keywords: | nonmonotone trust region method adaptive method indefinite dogleg path unconstrained minimization global convergence superlinear convergence |
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