向量值优化问题的适定性  

The Well-Posedness of Vector Optimization Problem

作　　者：滕岩梅[1] 王玉鹏[1] 

机构地区：[1]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《应用泛函分析学报》2014年第3期204-211,共8页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(10601005;61172060)

摘　　要：将向量值优化问题的适定性理论推广到具有W-距离的拟度量空间中,给出B-适定性及DH-适定性的概念,并得到相应的判别准则.定义一类非线性标量化函数,利用这类标量化函数的性质将向量值优化问题转化为标量值优化问题,得到原问题与标量化问题的适定性之间的等价关系.The notions of well-posedness for vector-valued optimization problem are extended to quasi-metric space with W-distance. We first give the definition of B-well-posedness and DH- well-posedness for vector-valued optimization problem, then sufficient and necessary conditions of B-well-posedness as well as DH-well-posedness are attained. By virtue of properties of the defined nonlinear scalarization function, we obtain some relationships of well-posedness between vector- valued optimization problem and the corresponding scalarized optimization problem.

关 键 词：W-距离 向量值优化问题 适定性 标量化 

分 类 号：O224[理学—运筹学与控制论] O177.32[理学—数学]