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http://dx.doi.org/10.4134/BKMS.2013.50.2.589

SOLVABILITY AND BOUNDEDNESS FOR GENERAL VARIATIONAL INEQUALITY PROBLEMS  

Luo, Gui-Mei (Department of Applied Mathematics Guangdong University of Finance)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 589-599 More about this Journal
Abstract
In this paper, we propose a sufficient condition for the existence of solutions to general variational inequality problems (GVI(K, F, $g$)). The condition is also necessary when F is a $g-P^M_*$ function. We also investigate the boundedness of the solution set of (GVI(K, F, $g$)). Furthermore, we show that when F is norm-coercive, the general complementarity problems (GCP(K, F, $g$)) has a nonempty compact solution set. Finally, we establish some existence theorems for (GNCP(K, F, $g$)).
Keywords
general variational inequality problem; general complementarity problem; existence; boundedness; strict feasibility; quasi-g-$P^M_*$ function;
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