Abstract
Strict feasibility is proved to be an equivalent characterization of (dual) variational inequalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This generalizes an earlier result from finite-dimensional Euclidean spaces to infinitedimensional reflexive Banach spaces. Moreover, the monotonicity-type assumptions are also mildly relaxed.
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This work is partially supported by NSFC(Grant A0324638), Sichuan Youth Science and Technology Foundation (06ZQ026-013), and SZD0406 from Sichuan Province
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He, Y.R., Mao, X.Z. & Zhou, M. Strict Feasibility of Variational Inequalities in Reflexive Banach Spaces. Acta Math Sinica 23, 563–570 (2007). https://doi.org/10.1007/s10114-005-0918-5
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DOI: https://doi.org/10.1007/s10114-005-0918-5
Keywords
- variational inequalities
- well-positioned sets
- barrier cone
- strict feasibility
- stably properly quasimonotone