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Zbl 1149.49009
Fang, Ya-Ping; Huang, Nan-Jing; Yao, Jen-Chih
Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems. (English)
[J] J. Glob. Optim. 41, No. 1, 117-133 (2008). ISSN 0925-5001; ISSN 1573-2916/e

Summary: We generalize the concept of well-posedness to a mixed variational inequality and give some characterizations of its well-posedness. Under suitable conditions, we prove that the well-posedness of a mixed variational inequality is equivalent to the well-posedness of a corresponding inclusion problem. We also discuss the relations between the well-posedness of a mixed variational inequality and the well-posedness of a fixed point problem. Finally, we derive some conditions under which a mixed variational inequality is well-posed.

MSC 2000:: *49J40 Variational methods including variational inequalities
49K40 Sensitivity of optimal solutions in the presence of perturbations
90C31 Sensitivity, etc.
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: mixed variational inequality; inclusion problem; fixed point problem; well-posedness

Cited in: Zbl 1177.49018

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