Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems. (English) Zbl 1149.49009

Fang, Ya-Ping; Huang, Nan-Jing; Yao, Jen-Chih

J. Glob. Optim. 41, No. 1, 117-133 (2008).

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:

49J40	Variational inequalities
49K40	Sensitivity, stability, well-posedness
90C31	Sensitivity, stability, parametric optimization
47H10	Fixed-point theorems

Keywords:

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

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