一类非凸向量优化问题关于真非控解的对偶理论  

Dual Theory of Properly Nondominated Solutions of a Class of Nonconvex Vector Optimization Problems with Variable Ordering Structures

作　　者：马俊涛 游曼雪 MA Juntao;YOU Manxue(School of Mathematic and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《保山学院学报》2025年第2期20-27,共8页JOURNAL OF BAOSHAN UNIVERSITY

基　　金：西华师范大学创新团队基金“优化理论、算法及应用”(项目编号:KCXTD2023-3)。

摘　　要：变动序优化问题在医学图像配准、投资组合优化、环境和行为科学等问题中具有重要应用。研究一类带变序结构的非凸约束向量优化问题,借助一个非线性标量化函数定义与原问题相关的实值增广拉格朗日函数,讨论拉格朗日函数的鞍点性质,根据拉格朗日函数的鞍点来刻画给定向量优化问题的Benson型真非控解。根据拉格朗日函数定义原向量优化问题相应的对偶集,并证明了相关的对偶性结果。The optimization problems with variable ordering structures has important applications in many fields,such as medical image registration,portfolio optimization,environmental and behavioral science.A class of non-convex vector optimization with variable ordering structures has been studied in this paper.With the help of a nonlinear scalar function,the real-valued augmented Lagrangian associated with the original problem has been defined.According to the saddle point of this Lagrangian,the properties of the saddle point of this Lagrangian is discussed,and the properly nondominated solution in the sense of Benson of a given vector optimization has been characterizied.A formal dual set is defined in terms of this Lagrangian,and some results for duality are obtained.

关 键 词：向量优化 变序结构 增广拉格朗日函数:鞍点 对偶性 

分 类 号：O17[理学—数学]