Abstract
In this paper, we give sufficient conditions for the existence of efficient solutions of a generalized vector quasi-equilibrium problem in topological vector spaces. The motivations for introducing this problem come from practical problems in traffic networks and the optimal control theory for discrete-time dynamical systems. The main results of the paper are proven with the help of a strongly monotonic function which can be constructed from the data of the problem under consideration. Some notions of cone-semicontinuity of set-valued maps, weaker than the usual concepts of semicontinuity, are also used in our study. As applications, we obtain existence results in vector quasi-optimization problems, Stampacchia set-valued vector quasi-variational inequality problems and Pareto vector quasi-saddle point problems. All these results are different from the corresponding ones in the literature.
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This research is funded by Vietnam National Foundation for Science and Technology (NAFOSTED).
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Minh, N.B., Tuan, L.A. & Sach, P.H. Efficiency in vector quasi-equilibrium problems and applications. Positivity 18, 531–556 (2014). https://doi.org/10.1007/s11117-013-0260-6
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DOI: https://doi.org/10.1007/s11117-013-0260-6
Keywords
- Vector quasi-equilibrium problem
- Optimal control theory
- Vector quasi-optimization problem
- Pareto vector quasi-saddle point
- Cone-semicontinuity
- Set-valued map