半严格-(B,G)-半预不变凸规划的Wolfe对偶问题  

Wolfe Duality Problem with Semistrict-( B,G)-Semi-Preinvex Programming

作　　者：孙佳徽 邵重阳 王泾晶 SUN Jiahui;SHAO Chongyang;WANG Jingjing(School of Management,Xi’an Polytechnic University,Xi’an 710048,China;College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]西安工程大学管理学院,西安710048 [2]重庆交通大学数学与统计学院,重庆400074

出　　处：《重庆理工大学学报（自然科学）》2020年第4期267-272,共6页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金项目(11401058);重庆市自然科学基金项目(cstc2018jcyj0337);重庆市科研创新团队项目(CXTDX201601022);重庆交通大学科研基金项目(2018PY21,201810618104);重庆交通大学研究生教育创新基金项目(2019S0123)。

摘　　要：讨论了与半严格-(B,G)-半预不变凸函数有关的可微多目标规划问题(TP),及其相对应的Wolfe型对偶问题(TW)之间可行解与弱Pareto解的关系。给出了目标函数和约束函数均为可微的半严格-(B,G)-半预不变凸函数的多目标规划问题的弱对偶、强对偶和逆对偶定理。其结果拓展了已有文献中与广义凸规划相关的Wolfe对偶结论,具有一般性。The differentiable multi-objective programming problems( TP) of semistrict-( B,G)-semi-preinvex function and the relationship between feasible solutions and weak pareto-optimal solutions for its Wolfe duality problems( TW) are discussed here. The weak duality,strong duality and inverse duality theorems for multi-objective programming problems with differentiable semistrict-( B,G)-semi-preinvex objective and constraint functions are established. The results extend the Wolfe duality results related to generalized convex programming in the literature and have generality.

关 键 词：半不变凸集 半严格-(B G)-半预不变凸函数 多目标规划 Wolfe对偶 

分 类 号：O221.6[理学—运筹学与控制论]