TITLE:
On the Well-Posedness for Optimization Problems: A Theoretical Investigation
AUTHORS:
Rosa Ferrentino, Carmine Boniello
KEYWORDS:
Well-Posedness, Hadamard and Tykhonov Well-Posedness, Vector Optimization Problems, Scalarization Function
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.1,
January
31,
2019
ABSTRACT: 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.