Quasi-P*-Maps, P(τ, α, β)-Maps, Exceptional Family of Elements, and Complementarity Problems

Y. B. Zhao and G. Isac
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Y. B. Zhao: Chinese Academy of Sciences
G. Isac: Royal Military College of Canada

Journal of Optimization Theory and Applications, 2000, vol. 105, issue 1, No 11, 213-231

Abstract: Abstract Quasi-P*-maps and P(τ, α, β)-maps defined in this paper are two large classes of nonlinear mappings which are broad enough to include P*-maps as special cases. It is of interest that the class of quasi-P*-maps also encompasses quasimonotone maps (in particular, pseudomonotone maps) as special cases. Under a strict feasibility condition, it is shown that the nonlinear complementarity problem has a solution if the function is a nonlinear quasi-P*-map or P(τ, α, β)-map. This result generalizes a classical Karamardian existence theorem and a recent result concerning quasimonotone maps established by Hadjisawas and Schaible, but restricted to complementarity problems. A new existence result under an exceptional regularity condition is also established. Our method is based on the concept of exceptional family of elements for a continuous function, which is a powerful tool for investigating the solvability of complementarity problems.

Keywords: nonlinear complementarity problems; exceptional family of elements; quasi-P*-maps; P(τ; α; β)-maps; exceptional regularity (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (5)

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DOI: 10.1023/A:1004674330768

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