On the Well-Posedness for Optimization Problems: A Theoretical Investigation

• 作者: Carmine Boniello Rosa Ferrentino
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: WELL-POSEDNESS HADAMARD and Tykhonov WELL-POSEDNESS VECTOR Optimization PROBLEMS SCALARIZATION FUNCTION
• 年，卷（期）: yysxyw_2019,（1）
• 页码范围: 19-38
• 页数: 20页
• 分类号: O1

摘要

In this paper, some theoretical notions of well-posedness and of well-posedness in the generalized sense for scalar optimization problems are presented and some important results are analysed. Similar notions of well-posedness, respectively for a vector optimization problem and for a variational inequality of differential type, are discussed subsequently and, among the various vector well-posedness notions known in the literature, the attention is focused on the concept of pointwise well-posedness. Moreover, after a review of well-posedness properties, the study is further extended to a scalarizing procedure that preserves well-posedness of the notions listed, namely to a result, obtained with a special scalarizing function, which links the notion of pontwise well-posedness to the well-posedness of a suitable scalar variational inequality of differential type.