대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제48권6호
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  • Pages.1225-1233
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  • 2011
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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CONNECTEDNESS AND COMPACTNESS OF WEAK EFFICIENT SOLUTIONS FOR VECTOR EQUILIBRIUM PROBLEMS

  • Long, Xian Jun (College of Mathematics and Statistics Chongqing Technology and Business University) ;
  • Peng, Jian Wen (Department of Mathematics Chongqing Normal University)
  • 투고 : 2010.07.07
  • 발행 : 2011.11.30
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⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. 133 (2007), 151-161].

키워드

참고문헌

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  9. X. H. Gong and J. C. Yao, Connectedness of the set of efficient solutions for generalized systems, J. Optim. Theory Appl. 138 (2008), no. 2, 189-196. https://doi.org/10.1007/s10957-008-9378-2
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  11. Y. D. Hu, The efficiency Theory of Multiobjective Programming, Shanghai: Shanghai Science and Technology Press, 1994.
  12. G. M. Lee, D. S. Kim, B. S. Lee, and N. D. Yun, Vector variational inequality as a tool for studying vector optimization problems, Nonlinear Anal. 34 (1998), no. 5, 745-765. https://doi.org/10.1016/S0362-546X(97)00578-6
  13. X. J. Long, N. J. Huang, and K. L. Teo, Existence and stability of solutions for generalized strong vector quasi-equilibrium problems, Math. Comput. Modelling 47 (2008), no. 3-4, 445-451. https://doi.org/10.1016/j.mcm.2007.04.013
  14. D. T. Luc, Theory of Vector Optimization, Lecture Notes in Economics and Mathematics Systems, Vol. 319, Springer-Verlag, New York, 1989.

피인용 문헌

  1. Existence-stability theorems for strong vector set-valued equilibrium problems in reflexive Banach spaces vol.2015, pp.1, 2015, https://doi.org/10.1186/s13660-015-0760-y
  2. Feasibility-solvbility theorems for generalized vector equilibrium problem in reflexive banach spaces vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-1812-2012-38
  3. Sensitivity analysis for generalized quasi-variational relation problems in locally G-convex spaces vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-1812-2012-158
  4. Existence conditions for symmetric generalized quasi-variational inclusion problems vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-40