有限理性与参数向量优化问题的良定性  

Bounded Rationality and Well Posedness of Parametric Vector Optimization Problems

作　　者：邓喜才[1] 左羽[1] 

机构地区：[1]贵州师范学院数学与计算机系,贵州贵阳550018

出　　处：《四川师范大学学报（自然科学版）》2015年第5期656-661,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然基金(11161008);教育部博士点基金(20115201110002);贵州省科学技术基金([2012]2289和[2012]2235)

摘　　要：最优化问题的良定性主要包括Tykhonov良定性和Hadamard良定性.近年来,随着向量优化问题的提出,对向量优化问题的良定性研究是一个相当活跃的领域.首先,通过非线性标量化技巧定义参数向量优化问题的有限理性模型.然后,利用这个模型给出参数向量优化问题的Tykhonov良定性和Hadamard良定性概念,并且更进一步的统一2种不同类型的良定性概念.最后,给出参数向量优化问题的各种良定性的充分条件.到目前为止还没有关于参数向量优化问题的良定性研究结果,因此对此类问题的良定性研究是有意义的.Tykhonov and Hadamard well-posedness are two main concepts for well-posed optimization problems. Recently,vector optimization problems have been intensively developed and many researchers have studied well-possedness for vector optimization problems. We first establish the bounded rationality model for parametric vector optimization problems by using a nonlinear scalarization technique. By using the model,we introduce the notions of Hadamard and Tykhonov well-posedness for parametric vector optimization problems. Moreover,a new well-posedness concept,which unifies two different notions of well-posedness is obtained. Finally,sufficient conditions on the well-posedness for parametric vector optimization problems are presented. So far,there are no results on wellposedness for parametric vector optimization problems,and it is very interesting to study this problem.

关 键 词：有限理性模型 非线性标量化技巧 良定性 参数向量优化问题 

分 类 号：O177.91[理学—数学]