Contributed Papers

Journal of Optimization Theory and Applications

, Volume 89, Issue 3, pp 749-769

On vector variational inequalities

  • S. J. YuAffiliated withDepartment of Applied Mathematics, National Sun Yat-Sen University
  • , J. C. YaoAffiliated withDepartment of Applied Mathematics, National Sun Yat-Sen University

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Abstract

In this paper, we study vector variational inequalities. The concept of weaklyC-pseudomonotone operator is introduced. By employing the Fan lemma, we establish several existence results. The new results extend and unify existence results of vector variational inequalities for monotone operators under a Banach space setting. In particular, existence results for the generalized vector complementarity problem with weaklyC-pseudomonotone operators in Banach space are obtained.

Key Words

Vector variational inequalities generalized vector complementarity problems weaklyC-pseudomonotone operators weakly (C +)-pseudomonotone operators weaklyv-coercive conditions generalizedL-condition