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.
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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.
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This work was supported in part by the National Science Foundation, Grant No. GP-34619.
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Karamardian, S. Complementarity problems over cones with monotone and pseudomonotone maps. J Optim Theory Appl 18, 445–454 (1976). https://doi.org/10.1007/BF00932654
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DOI: https://doi.org/10.1007/BF00932654