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

AM > Vol.10 No.1, January 2019

Applied Mathematics

Volume 10, Issue 1 (January 2019)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

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

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DOI: 10.4236/am.2019.101003 882 Downloads 2,219 Views Citations

Author(s)

Rosa Ferrentino¹, Carmine Boniello²

Affiliation(s)

¹Department of Economic and Statistics Sciences, University of Salerno, Fisciano, Salerno, Italy.
²University of Salerno, Fisciano, Salerno, Italy.

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.

KEYWORDS

Well-Posedness, Hadamard and Tykhonov Well-Posedness, Vector Optimization Problems, Scalarization Function

Share and Cite:

Ferrentino, R. and Boniello, C. (2019) On the Well-Posedness for Optimization Problems: A Theoretical Investigation. Applied Mathematics, 10, 19-38. doi: 10.4236/am.2019.101003.

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