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.
出处
《四川师范大学学报（自然科学版）》
CAS
北大核心
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)
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
bounded rationality model
nonlinear scalarization technique
well-posedness
parametric vector optimization problems
