| 等式与界约束非线性优化信赖域算法的全局收敛 |
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| 引用本文： | 童小娇,周叔子.等式与界约束非线性优化信赖域算法的全局收敛[J].高校应用数学学报(英文版),2003,18(1):83-94. |
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| 作者姓名： | 童小娇 周叔子 |
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| 作者单位： | Tong Xiaojiao Zhou ShuziDept. of Math.，Changsha Univ. of Electric Power，Changsha 410077，China. Dept. of Appl. Math.，Hunan Univ.，Changsha 410082，China. |
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| 摘 要： | § 1 ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉｚａｔｉｏｎｐｒｏｂｌｅｍ :ｍｉｎｉｍｉｚｅｆ(ｘ)ｓｕｂｊｅｃｔｔｏＣ(ｘ) =0 , ａ≤ｘ≤ｂ ,( 1 .1 )ｗｈｅｒｅｆ(ｘ) :Ｒｎ→Ｒ ,Ｃ(ｘ) =(ｃ1(ｘ) ,ｃ2 (ｘ) ,...,ｃｍ(ｘ) ) Ｔ:Ｒｎ→Ｒｍ ａｒｅｔｗｉｃｅｃｏｎｔｉｎｕｏｕｓｌｙｄｉｆｆｅｒｅｎｔｉａｂｌｅ,ｍ≤ｎ ,ａ ,ｂ∈Ｒｎ.Ｔｒｕｓｔｒｅｇｉｏｎａｌｇｏｒｉｔｈｍｓａｒｅｖｅｒｙｅｆｆｅｃｔｉｖｅｆｏｒｓｏｌｖｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉ…
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| 收稿时间： | 7 January 2002 |
Global convergence of trust region algorithm for equality and bound constrained nonlinear optimization |
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| Tong Xiaojiao,Zhou Shuzi.Global convergence of trust region algorithm for equality and bound constrained nonlinear optimization[J].Applied Mathematics A Journal of Chinese Universities,2003,18(1):83-94. |
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| Authors: | Tong Xiaojiao Zhou Shuzi |
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| Institution: | (1) Dept. of Math., Changsha Univ. of Electric Power, 410077 Changsha, China;(2) Dept. of Appl. Math., Hunan Univ., 410082 Changsha, China |
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| Abstract: | This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented. |
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| Keywords: | nonlinear optimization equality and bound constrained problem trust-region method global convergence |
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