On Generalized Convexity of Nonlinear Complementarity Functions

Miri, S.M.; Effati, Sohrab

doi:10.1007/s10957-014-0553-3

Cited by 10 publications

(2 citation statements)

References 13 publications

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“…In this paper, we establish that the result done by Miri and Effati's in [21] also holds for general complementarity functions associated with the GCP. Since the GCP includes NCP, SDCP, SOCCP, and SCCP as special cases, this is indeed a nice property for a wide range of complementarity problems.…”

Section: Final Remarksupporting

confidence: 63%

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Differentiability v.s. convexity for complementarity functions

2015

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It is known that complementarity functions play an important role in dealing with complementarity problems. The most well known complementarity problem is the symmetric cone complementarity problem (SCCP) which includes nonlinear complementarity problem (NCP), semidefinite complementarity problem (SDCP), and second-order cone complementarity problem (SOCCP) as special cases. Moreover, there is also socalled generalized complementarity problem (GCP) in infinite dimensional space. Among the existing NCP-functions, it was observed that there are no differentiable and convex NCP-functions. In particular, Miri and Effati [20] show that convexity and differentiability cannot hold simultaneously for an NCP-function. In this paper, we further establish that such result also holds for general complementarity functions associated with the GCP.

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Section: Final Remarksupporting

confidence: 63%

“…Among the existing NCP-functions, it is observed that none of them is both convex and differentiable. In fact, Miri and Effati [21] show that there is no pseudoconvex NCP-function, which implies that the convexity and differentiability cannot hold simultaneously for a NCP function. The proof is based on the following lemmas.…”

Section: Introductionmentioning

confidence: 99%