不确定信息下分式半无限优化问题的近似最优性刻画  

Characterizations of Approximate Optimality Conditions for Fractional Semi-Infinite Optimization Problems With Uncertainty

作　　者：冯欣怡 孙祥凯 FENG Xinyi;SUN Xiangkai(Chongqing Key Laboratory of Social Economy and Applied Statistics,School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,P.R.China)

机构地区：[1]重庆工商大学数学与统计学院经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《应用数学和力学》2022年第6期682-689,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11701057);重庆市自然科学基金(cstc2020jcyj-msxmX0016);重庆市重点实验室开放课题(KFJJ2019097);重庆市巴渝学者青年学者项目。

摘　　要：该文研究了一类带不确定参数的多目标分式半无限优化问题.首先借助鲁棒优化方法,引入该不确定多目标分式优化问题的鲁棒对应优化模型,并借助Dinkelbach方法,将该鲁棒对应优化模型转化为一般的多目标优化问题.随后借助一种标量化方法,建立了该优化问题的标量化问题,并刻画了它们的解之间的关系.最后借助一类鲁棒型次微分约束规格,建立了该不确定多目标分式优化问题拟近似有效解的鲁棒最优性条件.A class of multi-objective fractional semi-infinite optimization problems with uncertain data were investigated.Firstly, a robust optimization model corresponding to the uncertain multi-objective optimization problem was introduced.Then the optimization model was converted to a multi-objective optimization problem with the Dinkelbach method. In turn,by means of the scalarization method, the corresponding scalarization optimization problem was built, and the relationship between robust solutions to the multi-objective optimization problem and its corresponding scalarization optimization problem was described. Finally, through a robust-type sub-differential constraint qualification, the robust optimality condition for approximate quasi-efficient solutions to the multi-objective fractional optimization problem was established.

关 键 词：多目标优化 鲁棒优化 拟有效解 最优性条件 

分 类 号：O221.6[理学—运筹学与控制论] O224[理学—数学]