同伦内点方法求解一类无界非凸集合上的不动点问题

J4 ›› 2011, Vol. 49 ›› Issue (05): 839-843.

同伦内点方法求解一类无界非凸集合上的不动点问题

苏孟龙^1,2, 赵立芹³, 吕显瑞²

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

收稿日期:2011-03-18 出版日期:2011-09-26 发布日期:2011-09-27
通讯作者: 苏孟龙 E-mail:mlsulynu@163.com

Homotopy Interior Point Method for Solving a Class ofFixed Point Problems in Unbounded Nonconvex Sets

SU Menglong^1,2, ZHAO Liqin³, L Xianrui²

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

Received:2011-03-18 Online:2011-09-26 Published:2011-09-27
Contact: SU Menglong E-mail:mlsulynu@163.com

摘要/Abstract

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.

关键词: 同伦内点方法, 无界非凸集, 全局收敛性方法

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.

Key words: homotopy interior point method, unbounded nonconvex sets, globally convergent method

中图分类号:

O221.2

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]. J4, 2011, 49(05): 839-843.

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]. J4, 2011, 49(05): 839-843.

[1]	苏孟龙, 吕显瑞. 同伦内点方法求解一类无界区域上的多目标规划问题[J]. 吉林大学学报(理学版), 2019, 57(06): 1367-1371.
[2]	赵雪, 张春阳, 张树功. 弱拟法锥条件下解多目标规划问题的同伦方法[J]. J4, 2012, 50(4): 663-666.