On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method

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• 作者：Ali Farajzadeh ; Byung Soo Lee…
• 关键词：Scalarization function ; Generalized vector quasi ; equilibrium ; System of generalized vector quasi ; equilibrium ; Topological vector space ; 90C47 ; 90C33
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：168
• 期：2
• 页码：584-599
• 全文大小：453 KB
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• 作者单位：Ali Farajzadeh (1)
  Byung Soo Lee (2)
  Somyot Plubteing (3)
  
  1. Department of Mathematics, Razi University, Kermanshah, 67149, Iran
  2. Department of Mathematics, Kyungsung University, Busan, 608-736, Republic of Korea
  3. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

In this paper, we consider the nonlinear scalarization function in the setting of topological vector spaces and present some properties of it. Moreover, using the nonlinear scalarization function and Fan–Glicksberg–Kakutani’s fixed point theorem, we obtain an existence result of a solution for a generalized vector quasi-equilibrium problem without using any monotonicity and upper semi-continuity (or continuity) on the given maps. Our result can be considered as an improvement of the known corresponding result. After that, we introduce a system of generalized vector quasi-equilibrium problem which contains Nash equilibrium and Debreu-type equilibrium problem as well as the system of vector equilibrium problem posed previously. We provide two existence theorems for a solution of a system of generalized vector quasi-equilibrium problem. In the first one, our multi-valued maps have closed graphs and the maps are continuous, while in the second one, we do not use any continuity on the maps. Moreover, the method used for the existence theorem of a solution of a system of generalized vector quasi-equilibrium problem is not based upon a maximal element theorem. Finally, as an application, we apply the main results to study a system of vector optimization problem and vector variational inequality problem. Keywords Scalarization function Generalized vector quasi-equilibrium System of generalized vector quasi-equilibrium Topological vector space