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Zbl 1047.90067
Lemaire, B.; Salem, C. Ould Ahmed; Revalski, J. P.
Well-posedness by perturbations of variational problems. (English)
[J] J. Optimization Theory Appl. 115, No. 2, 345-368 (2002). ISSN 0022-3239; ISSN 1573-2878/e

Summary: In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.

MSC 2000:: *90C31 Sensitivity, etc.
58E30 Variational principles on infinite-dimensional spaces

Keywords: Well-posedness; convex functions; subdifferentials; optimization; maximal monotone operators; Yosida regularization; inclusion; fixed points

Cited in: Zbl 1164.47351

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