拟法锥条件下带均衡约束多目标规划问题的同伦方法

详细信息    查看全文 | 推荐本文 |

英文篇名：Homotopy Method for Multi-Objective Programming Problems with Equilibrium Constraints under Quasi-Normal Cone Condition 作者：赵雪 ; 高静 ; 杨月婷 英文作者：Zhao Xue;Gao Jing;Yang Yueting;School of Mathematics and Statistics,Beihua University; 关键词：多目标规划问题 ; 同伦内点算法 ; 拟法锥条件 ; 均衡约束 英文关键词：multi-objective programming problems;;homotopy interior point algorithm;;quasi-norm cone condition;;equilibrium constraints 中文刊名：ZLYY 英文刊名：Journal of Beihua University(Natural Science) 机构：北华大学数学与统计学院; 出版日期：2017-07-10 出版单位：北华大学学报(自然科学版) 年：2017 期：v.18 基金：国家自然科学基金项目(11171003);国家自然科学基金天元基金项目(11626037);; 吉林省教育厅科学技术研究项目(2015156) 语种：中文; 页：ZLYY201704001 页数：5 CN：04 ISSN：22-1316/N 分类号：6-10

摘要

利用组合同伦内点法给出了带均衡约束的多目标规划的求解问题,在合适的假设条件下,证明了该算法具有全局收敛性,数值例子表明该算法是合理有效的.
        The multi-objective programming problems with equilibrium constraints were given by means of homotopy interior point algorithm. We also prove the global convergence of this homotopy interior point algorithm under assumptions. Moreover,the results of the numeric example show that this method is feasible and effective.

引文

[1]Kellogg R B,Li T Y,Yorke J A.A constructive proof the Brouwer fixed-point theorem and computational results[J].SIAM J Numer Analysis,1976,18:473-483.
    [2]S Smale.A convergent process of price adjustment and global Newton method[J].J Math Econom,1976,3:1-14.
    [3]Chow S N,Mallet-Paret J,York J A.Finding zero of maps:Homotopy methods that are constructive with probability one[J].Math Comput,1978,32:887-899.
    [4]Zhao Xue,Zhang Shu-gong,Liu Qing-huai.A combined homotopy interior-point method for the linear complementarity problem[J].Journal of Information and Computational Science,2010,7(7):1589-1594.
    [5]X Zhao,S G Zhang,Q H Liu.Homotopy interior-point method for a general multi-objective programming problem[J].Journal of Applied Mathematics,2012:ID497345.
    [6]X Zhao,S G Zhang,Y T Yang,et al.Homotopy method for a general multi-objective programming problem under generalized quasi-normal cone condition[J].Abstract and Applied Analysis,2012:ID591612.
    [7]Liu Qing-huai,Yu Bo,Feng Guo-chen.An interior point path-following method for nonconvex programming with qusi-normal cone condition[J].Advances in Mathematics,2000,19(4):281-282.
    [8]张筑生.微分拓扑新讲[M].北京:北京大学出版社,2002.