同伦内点方法求解一类无界区域上的多目标规划问题

吉林大学学报(理学版) ›› 2019, Vol. 57 ›› Issue (06): 1367-1371.

同伦内点方法求解一类无界区域上的多目标规划问题

苏孟龙¹, 吕显瑞²

1. 洛阳师范学院数学学院, 河南洛阳 471934; 2. 吉林大学数学学院, 长春 130012

收稿日期:2019-06-17 出版日期:2019-11-26 发布日期:2019-11-21
通讯作者: 苏孟龙 E-mail:mlsulynu@163.com

Homotopy Interior Point Method for Solving a Class ofMultiobjective Programming Problems in Unbounded Regions

SU Menglong¹, LV Xianrui²

1. College of Mathematics, Luoyang Normal University, Luoyang 471934, Henan Province, China;
2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2019-06-17 Online:2019-11-26 Published:2019-11-21
Contact: SU Menglong E-mail:mlsulynu@163.com

摘要/Abstract

摘要： 提出一种求解一类无界约束集上多目标规划问题的同伦内点方法. 先利用目标函数的Hessian矩阵构造一组无界性条件, 并给出满足该条件的一个简单实例; 再证明连接给定初始点[KG*8]和多目标规划解点内路径的存在性; 最后给出同伦内点法的全局收敛性结果.

关键词: 多目标规划问题, 同伦内点方法, 无界性条件

Abstract: We proposed a homotopy interior point method for solving a class of the multiobjective programming problems in unbounded constrained sets. Firstly, by using the Hessian matrix of the objective function, we constructed a set of unboundedness conditions, and gave a simple example to illustrate these conditions. Secondly, we proved the existence of the interior path connecting a given initial point and a solution point of the multiobjective programming problems. Finally, we gave the global convergence results of the homotopy interior point method.

Key words: multiobjective programming problem, homotopy interior point method, unboundedness condition

中图分类号:

O221.2

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.

SU Menglong, LV Xianrui. Homotopy Interior Point Method for Solving a Class ofMultiobjective Programming Problems in Unbounded Regions[J]. Journal of Jilin University Science Edition, 2019, 57(06): 1367-1371.

[1]	赵雪, 杨月婷, 张树功. 同伦内点法求解多目标规划问题[J]. 吉林大学学报(理学版), 2013, 51(04): 551-554.
[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.
[3]	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.