Journal of Global Optimization

, Volume 68, Issue 3, pp 537–562 | Cite as

An approximate bundle method for solving nonsmooth equilibrium problems

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Abstract

We present an approximate bundle method for solving nonsmooth equilibrium problems. An inexact cutting-plane linearization of the objective function is established at each iteration, which is actually an approximation produced by an oracle that gives inaccurate values for the functions and subgradients. The errors in function and subgradient evaluations are bounded and they need not vanish in the limit. A descent criterion adapting the setting of inexact oracles is put forward to measure the current descent behavior. The sequence generated by the algorithm converges to the approximately critical points of the equilibrium problem under proper assumptions. As a special illustration, the proposed algorithm is utilized to solve generalized variational inequality problems. The numerical experiments show that the algorithm is effective in solving nonsmooth equilibrium problems.

Keywords

Equilibrium problems Bundle methods Approximate function and subgradient 

Mathematics Subject Classification

90C25 49J40 90C20 

Notes

Acknowledgements

The authors thank two anonymous referees for a number of valuable and helpful suggestions.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Fan-Yun Meng
    • 1
  • Li-Ping Pang
    • 1
  • Jian Lv
    • 1
  • Jin-He Wang
    • 2
  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianChina
  2. 2.School of ComputerQingdao Technological UniversityQingdaoChina

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