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Regularized gap functions and error bounds for generalized mixed strong vector quasiequilibrium problems

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Abstract

In this paper, we consider generalized mixed strong vector quasiequilibrium problems in infinite-dimensional spaces. Using the nonlinear scalarization method, we first propose gap functions for such problems. Then, based on the Moreau–Yosida regularization of these functions, we introduce regularized gap functions for the reference problems. Next, we study sufficient conditions for the mentioned functions to be continuous. Finally, error bounds for the concerning problems in terms of regularized gap functions are investigated. Some examples are provided to illustrate our results.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions that helped us significantly improve the presentation of our paper. This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 101.01-2017.18.

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Authors and Affiliations

  1. Department of Mathematics, Teacher College, Can Tho University, Can Tho, Vietnam

    Lam Quoc Anh

  2. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Van Hung

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Van Hung

  4. Department of Mathematics, Dong Thap University, 783 Pham Huu Lau Street, Ward 6, Cao Lanh City, Vietnam

    Vo Minh Tam

Authors
  1. Lam Quoc Anh
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  2. Nguyen Van Hung
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  3. Vo Minh Tam
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Correspondence to Nguyen Van Hung.

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Communicated by Hector Ramirez.

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Anh, L.Q., Van Hung, N. & Tam, V.M. Regularized gap functions and error bounds for generalized mixed strong vector quasiequilibrium problems. Comp. Appl. Math. 37, 5935–5950 (2018). https://doi.org/10.1007/s40314-018-0670-y

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  • DOI: https://doi.org/10.1007/s40314-018-0670-y

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