Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOLVABILITY AND BOUNDEDNESS FOR GENERAL VARIATIONAL INEQUALITY PROBLEMS

  • Luo, Gui-Mei (Department of Applied Mathematics Guangdong University of Finance)
  • Received : 2011.12.02
  • Published : 2013.03.31
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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

Acknowledgement

Supported by : NSF of China

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