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

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DOI: 10.4236/am.2019.101003    346 Downloads   572 Views Citations

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.

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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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