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Cavazzuti, E. and Morgan, J. (1983) Well-Posed Saddle Point Problems in Optimization, Theory and Algorithms. In: Hirriart-Urruty, J.B., Oettli, W. and Stoer, J., Eds., Optimization, Theory and Algorithms, Marcel Dekker, New York, 61-76.

has been cited by the following article:

• 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.