Acta Mathematica Sinica, English Series

, Volume 25, Issue 3, pp 343–354 | Cite as

Unconstrained optimization reformulations of equilibrium problems

  • Li Ping ZhangEmail author
  • Ji Ye Han


We generalize the D-gap function developed in the literature for variational inequalities to a general equilibrium problem (EP). Through the D-gap function, the equilibrium problem is cast as an unconstrained minimization problem. We give conditions under which any stationary point of the D-gap function is a solution of EP and conditions under which it provides a global error bound for EP. Finally, these results are applied to box-constrained EP and then weaker conditions are established to obtain the desired results for box-constrained EP.


equilibrium problems D-gap function error bound unconstrained optimization 

MR(2000) Subject Classification

90C30 90C31 90C33 49J52 


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingP. R. China
  2. 2.Institute of Applied Mathematics, Academy of Mathematics & Systems ScienceChinese Academy of SciencesBeijingP. R. China

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