| 同伦内点方法求解一类无界非凸集合上的不动点问题 |
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| 引用本文： | 苏孟龙,赵立芹,吕显瑞.同伦内点方法求解一类无界非凸集合上的不动点问题[J].吉林大学学报(理学版),2011,49(5):839-843. |
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| 作者姓名： | 苏孟龙 赵立芹 吕显瑞 |
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| 作者单位： | 1. 洛阳师范学院 数学学院, 河南 洛阳 471000,2. 吉林大学 数学学院, 长春 130012;3. 吉林大学 学报编辑部, 长春 130012 |
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| 基金项目： | 国家自然科学基金(批准号:11026079); 河南省高校青年骨干教师资助项目(批准号:173); 河南省基础与前沿技术研究项目(批准号:092300410187) |
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| 摘 要： | 给出了求解一类无界非凸集上不动点问题的同伦内点方法.利用自映射φ(x),并结合约束函数的梯度,先构造一组无界性条件,在此基础上,给出了不动点存在性的构造性证明,得到了同伦内点方法的全局收敛性.
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| 关 键 词： | 同伦内点方法 无界非凸集 全局收敛性方法 |
| 收稿时间： | 2011-03-18 |
Homotopy Interior Point Method for Solving a Class of Fixed Point Problems in Unbounded Nonconvex Sets |
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| SU Meng-Long,DIAO Li-Qin,LV Xian-Rui.Homotopy Interior Point Method for Solving a Class of Fixed Point Problems in Unbounded Nonconvex Sets[J].Journal of Jilin University: Sci Ed,2011,49(5):839-843. |
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| Authors: | SU Meng-Long DIAO Li-Qin LV Xian-Rui |
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| Institution: | 1. College of Mathematics, Luoyang Normal University, Luoyang 471000, Henan Province, China;2. College of Mathematics, Jilin University, Changchun 130012, China;3. Editorial Department of Journal of Jilin University, Changchun 130012, China |
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| Abstract: | A homotopy interior point method was proposed to solve fixed point problems in unbounded nonconvex sets. Combining the self mapping Φ(x) with the gradients of constrained functions, we constructed a set of unbounded conditions. Based on those unbounded conditions, we gave the constructive proof of the existence of fixed points, obtaining the global convergence results of the homotopy interior point method. |
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| Keywords: | homotopy interior point method unbounded nonconvex sets globally convergent method |
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