Continuity of Solution Maps to Parametric Set Optimization Problems via Parametric Equilibrium Problems

Abstract

In this paper, we consider set optimization problems with respect to set less order relations. We introduce nonlinear scalarization functions for sets and study several properties of such functions. Using the concerning functions, we investigate relationships between set optimization problems and equilibrium problems. Sufficient conditions for the continuity of solution maps to such problems via equilibrium problems are established.

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Acknowledgments

The authors would like to thank the anonymous referees for their valuable remarks and suggestions which have helped us improve the paper.

Funding

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2020.11.

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Correspondence to Tran Ngoc Tam.

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Dedicated to Professor Hoang Tuy on the occasion of his 90th birthday

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Anh, L.Q., Danh, N.H. & Tam, T.N. Continuity of Solution Maps to Parametric Set Optimization Problems via Parametric Equilibrium Problems. Acta Math Vietnam 45, 383–395 (2020). https://doi.org/10.1007/s40306-020-00370-6

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Keywords

  • Set optimization problem
  • Equilibrium problem
  • Nonlinear scalarization
  • Stability
  • Hausdorff continuity

Mathematics Subject Classification (2010)

  • 49K40
  • 90C31
  • 91B50