Operations Research Transactions ›› 2014, Vol. 18 ›› Issue (1): 113-133.

• Original Articles • Previous Articles     Next Articles

Several developments of variational inequalities and complementarity problems, bilevel programming and MPEC

HUANG Zhenghai1, LIN Guihua2, XIU Naihua3,*   

  1. 1. Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China; 2. School of Management, Shanghai University, Shanghai 200444,  China; 3. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, China
  • Online:2014-03-15 Published:2014-03-15

Abstract: This paper investigates finite-dimensional variational inequalities and complementarity problems, bilevel programming problems and mathematical programs with equilibrium constraints (MPECs).  After a brief introduction to these problems, this paper focuses on several recent rapidly developing aspects in these fields, which include theories and methods for symmetric cone complementarity problems, projection and contraction methods for variational inequality problems, models and methods for stochastic variational inequalities and stochastic complementarity problems, and new methods for bilevel programming problems and MPECs. Finally, several future research directions are proposed in this paper.

Key words: variational inequality, complementarity problem, bilevel programming, mathematical program with equilibrium constraints

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