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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References
Habetler, G. J., andPrice, A. L. Existence Theory for Generalized Nonlinear Complementarity Problems, Journal of Optimization Theory and Applications, Vol. 7, No. 4, 1971.
Karamardian, S. Generalized Complementarity Problem, Journal of Optimization Theory and Applications, Vol. 8, No. 3, 1971.
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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
Key Words
- Nonlinear complementarity problems over cones
- pseudomonotone maps
- mathematical programming
- variational inequalities
- duality theory