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Complementarity problems over cones with monotone and pseudomonotone maps

  • S. Karamardian
Contributed Papers

Abstract

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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References

  1. 1.
    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
  2. 2.
    Karamardian, S. Generalized Complementarity Problem, Journal of Optimization Theory and Applications, Vol. 8, No. 3, 1971.Google Scholar
  3. 3.
    Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.Google Scholar
  4. 4.
    Moré, J. J. Classes of Functions and Feasibility Conditions in Nonlinear Complementarity Problems, Cornell University, Ithaca, New York, Department of Computer Sciences, TR No. 73-174, 1973.Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

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

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