Strict feasibility and stable solvability of bifunction variational inequalities. (English) Zbl 1227.49015
Summary: We study strict feasibility of a bifunction variational inequality. It is proved that a monotone bifunction variational inequality has a nonempty and bounded solution set if and only if it is strictly feasible. Stable solvability of the bifunction variational inequality is discussed under strict feasibility assumption when the domain set is perturbed. Our results generalize earlier results on the classical variational inequality to the case of the bifunction variational inequality.
MSC:
| 49J40 | Variational inequalities |
| 49K40 | Sensitivity, stability, well-posedness |
| 58E35 | Variational inequalities (global problems) in infinite-dimensional spaces |
Keywords:
bifunction variational inequalities; strict feasibility; monotonicity; nonemptiness and boundedness of solution sets; stable solvabilityReferences:
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