Differentiability v.s. convexity for complementarity functions

Chien Hao Huang, Jein Shan Chen, Juan Enrique Martinez-Legaz

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)


© 2015, Springer-Verlag Berlin Heidelberg. 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 so-called 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 (J Optim Theory Appl 164:723–730, 2015) 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.
Original languageEnglish
Pages (from-to)209-216
JournalOptimization Letters
Issue number1
Publication statusPublished - 1 Jan 2017


  • Closed convex cone
  • Complementarity functions
  • NCP-functions
  • Second-order cone


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