| 求解一类约束优化信赖域方法的子问题 |
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| 引用本文： | 崔颖川. 求解一类约束优化信赖域方法的子问题[J]. 高等学校计算数学学报, 1999, 21(1): 71-80 |
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| 作者姓名： | 崔颖川 |
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| 作者单位： | 南京大学数学系!南京，210093 |
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| 基金项目： | 国家自然科学基金!（19671014） |
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| 摘 要： | １引言设Ｈ为一给定的ｎ×ｎ对称矩阵，ｃＲ＂，本文考虑如｝的约束优化问题这里ａ＞０为给定的参数，Ｃ＝｛ｘＲｎｘ＜ａ是Ｒ”中的一个球体，Ｋ是一个简单凸闭集．当Ｋ＝Ｒｎ时，问题（Ｐ）便是无约束优化的信赖域子问题．当Ｋ＝｛ｘＲｎμ≤ｘ≤υ５，（μ１，μ２，…，μｎ）Ｔ，υ＝（υ１，υ２…，υｎ）Ｔ，且—∞＜μｉ＜υｉ＜ｖ＜＋∞，ｉ＝１，２，…，ｎ时，问题（Ｐ）便是用信赖域方法求解带上下界约束的优化问题时遇到的子问题．对于无约束信赖域方法的子问题已经有了比较成熟的算法［８，１２－１３，１５－１６］．Ｋ＝Ｒ…
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| 关 键 词： | 约束优化 信赖域法 子问题 最佳化 |
SOLVING A SUBPROBLEM IN TRUST REGION APPROACH FOR A CLASS OF CONSTRAINED OPTIMIZATION PROBLEMS |
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| Cui Yingchuan. SOLVING A SUBPROBLEM IN TRUST REGION APPROACH FOR A CLASS OF CONSTRAINED OPTIMIZATION PROBLEMS[J]. Numerical Mathematics A Journal of Chinese Universities, 1999, 21(1): 71-80 |
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| Authors: | Cui Yingchuan |
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| Affiliation: | Nanjing University |
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| Abstract: | In this paper, we present a method for solving tile basic problem in the trust region approach for optimization problem with simple bounds constraints. This method exploits the advantages of Gabay's decomposition method and the Projection and Contraction (PC) method. In fact. when the treated problem is solved by Gabay's decomposition method. the main work at each iteration is to solve a 'wellconditioned' linear variational inequality, which can be solved by the Projection and Contraction method efficiently. Some numerical tests show that the method is applicable. |
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| Keywords: | trust region approach variational inequality projection and contraction method Gabay's decomposition method. |
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