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A Predictor‐Corrector Method for Solving Equilibrium Problems

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Listed:
  • Zong-Ke Bao
  • Ming Huang
  • Xi-Qiang Xia

Abstract

We suggest and analyze a predictor‐corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new prediction. At the same time, we present convergence analysis under perfect foresight and imperfect one. In particular, we introduce a stopping criterion which gives rise to Δ‐stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities.

Suggested Citation

  • Zong-Ke Bao & Ming Huang & Xi-Qiang Xia, 2014. "A Predictor‐Corrector Method for Solving Equilibrium Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:313217
    DOI: 10.1155/2014/313217
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    References listed on IDEAS

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    1. Jonathan Eckstein, 1993. "Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 202-226, February.
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