Complementarity problems over cones with monotone and pseudomonotone maps

  • S. Karamardian
Contributed Papers


The notion of a monotone map is generalized to that of a pseudomonotone map. It is shown that a differentiable, pseudoconvex function is characterized by the pseudomonotonicity of its gradient. Several existence theorems are established for a given complementarity problem over a certain cone where the underlying map is either monotone or pseudomonotone under the assumption that the complementarity problem has a feasible or strictly feasible point.

Key Words

Nonlinear complementarity problems over cones pseudomonotone maps mathematical programming variational inequalities duality theory 


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    Habetler, G. J., andPrice, A. L. Existence Theory for Generalized Nonlinear Complementarity Problems, Journal of Optimization Theory and Applications, Vol. 7, No. 4, 1971.Google Scholar
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    Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.Google Scholar
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Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • S. Karamardian
    • 1
  1. 1.University of California at IrvineIrvine

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