Stability and well-posedness in vector lexicographic equilibrium problems

Dang Thi My Van , Lam Quoc Anh * , Pham Thi Vui and Nguyen Thi Thao Truc

* Corresponding author (quocanh@ctu.edu.vn)

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Received: 18 Aug 2015
Revised: 16 Sep 2015
Accepted: 26 Nov 2015
Published: 19 Aug 2016
DOI: 10.22144/ctu.jen.2016.029
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Dang, T. M. V., Lam, Q. A., Pham, T. V., & Nguyen, T. T. T. (2016). Stability and well-posedness in vector lexicographic equilibrium problems. CTU Journal of Innovation and Sustainable Development , (03), 94-101. https://doi.org/10.22144/ctu.jen.2016.029
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No. 03 (2016)

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Abstract

In this paper we consider lexicographic vector equilibrium problems in metric spaces. Sufficient conditions for a family of such problems to be stable in the  sense of upper and lower semicontinuity of the solution sets are established. Moreover, we also derive necessary and/or sufficient conditions for lexicographic vector equilibrium problems to be well-posed  at the reference point. Many examples are provided to ensure the essentialness of the imposed assumptions.
Keywords: Lexicographic order, Equilibrium problems, Stability, (Uniquely/Hadamard) well-posedness, Semicontinuity, Continuity

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