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一类广义凸映射多目标有效解集的连通性

THE CONNECTEDNESS OF THE SET OF EFFICIENT SOLUTIONS OF A KIND OF GENERAL CONVEX MULTIPLI PROGRAMMING OPTIMIGATION
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摘要 本文在S.Helbleg工作的基础上,进一步研究了有效解集的连通问题,得到了当映射为严格逐点拟凸时,有效解集不但连通,而且路连通。 In this paper, On the base of S. Helbleg's work [5], the author studies futher thequastion that the connectedness of the Set of efficient Soluitons, and obtain that when themapping is a strictly quasiconvex, the set of efficient solutions is not only Connected, but also path Connected.
作者 周昆平
机构地区 南昌大学数学系
出处 《南昌大学学报(理科版)》 CAS 1993年第3期99-103,共5页 Journal of Nanchang University(Natural Science)
关键词 逐点拟凸 有效解集 路连通 凸映射 strictly quasiconvex efficient sdution path connected
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参考文献5

  • 1胡毓达,孙尔江.严格拟凹集合的有效点集和严格拟凹多目标规划有效解集的连通性[J]科学通报,1990(15).
  • 2胡毓达,胡一凡.锥拟凸与拓扑向量空间多目标最优化有效解集和弱有效解集的连通性[J].应用数学学报,1989,12(1):115-123. 被引量:21
  • 3S. Helbig. On the connectedness of the set of weakly efficient points of a vector optimization problem in locally convex spaces[J] 1990,Journal of Optimization Theory and Applications(2):257~270
  • 4A. R. Warburton. Quasiconcave vector maximization: Connectedness of the sets of Pareto-optimal and weak Pareto-optimal alternatives[J] 1983,Journal of Optimization Theory and Applications(4):537~557
  • 5P. H. Naccache. Connectedness of the set of nondominated outcomes in multicriteria optimization[J] 1978,Journal of Optimization Theory and Applications(3):459~467

二级参考文献3

  • 1A. R. Warburton. Quasiconcave vector maximization: Connectedness of the sets of Pareto-optimal and weak Pareto-optimal alternatives[J] 1983,Journal of Optimization Theory and Applications(4):537~557
  • 2G. R. Bitran,T. L. Magnanti. The structure of admissible points with respect to cone dominance[J] 1979,Journal of Optimization Theory and Applications(4):573~614
  • 3P. H. Naccache. Connectedness of the set of nondominated outcomes in multicriteria optimization[J] 1978,Journal of Optimization Theory and Applications(3):459~467

共引文献20

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