一类弱齐次向量优化问题解集的非空有界性  

On the nonemptiness and boundedness of solution sets for weakly homogeneous vector optimization problems

作　　者：邹萌 李耿华 ZOU Meng;LI Genghua(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《内江师范学院学报》2024年第4期20-25,共6页Journal of Neijiang Normal University

基　　金：重庆市自然科学基金项目(cstc2020jcyj-msxmX0231);重庆工商大学高层次人才科研启动项目(2056007)。

摘　　要：弱齐次向量优化问题是一类非凸向量优化问题.利用渐近锥和渐近函数,给出了弱齐次向量优化问题的强型和弱型正则性条件,并讨论其性质.在正则性条件下,研究了弱齐次向量优化问题(弱)Pareto有效解集的非空性和有界性.此外,还提出了解集非空有界性的一个新的充分性条件,并讨论了它与强正则性条件的关系.Weakly homogeneous vector optimization is a class of nonconvex vector optimization problems.Based on the asymptotic cone and asymptotic function,strong and weak regularity conditions for weakly homogeneous vector optimization problem are given,and their properties are discussed.Under the regularity conditions,the nonemptiness and boundedness of(weakly)Pareto efficient solution set for weakly homogeneous vector optimization problems are studied.Furthermore,a new sufficient condition for the nonemptiness and boundedness of the solution set is proposed,and its relationship with the strong regular condition is discussed.

关 键 词：向量优化 渐近函数 正则性条件 非空性 有界性 

分 类 号：O221.6[理学—运筹学与控制论] O224[理学—数学]