Efficiency in vector quasi-equilibrium problems and applications
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.
KeywordsVector quasi-equilibrium problem Optimal control theory Vector quasi-optimization problem Pareto vector quasi-saddle point Cone-semicontinuity Set-valued map
Mathematics Subject Classification (2000)49J53 54H25
This research is funded by Vietnam National Foundation for Science and Technology (NAFOSTED).
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