Well-posedness by perturbations of variational problems. (English) Zbl 1047.90067

Lemaire, B.; Salem, C. Ould Ahmed; Revalski, J. P.

J. Optimization Theory Appl. 115, No. 2, 345-368 (2002).

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:

90C31	Sensitivity, stability, parametric optimization
58E30	Variational principles in infinite-dimensional spaces

Keywords:

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

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