On the Density of Henig Efficient Points in Locally Convex Topological Vector Spaces

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• 作者：Joseph Newhall ; Robert K. Goodrich
• 关键词：Henig efficient point ; Regular efficient point ; Asymptotic cone ; Asymptotically compact set ; Density results ; 46A03 ; 46N10
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：165
• 期：3
• 页码：753-762
• 全文大小：389 KB
• 参考文献：1.Daniilidis, A.: Arrow-barankin-blackwell theorems and related results in cone duality: a survey. In: Nguyen, V.H., Strodiot, J.-J., Tossings, P. (eds.) Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 481, pp. 119-31. Springer, Berlin, Heidelberg (2000)
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  11.Z?linescu, C.: Stability for a class of nonlinear optimization problems and applications. Lectures to the International School of Mathematics, Erice Sicily (1988)
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  15.G?pfert, A., Riahi, H., Tammer, C., Z?linescu, C.: Variational Methods in Partially Ordered Spaces. Canadian Mathematical Society, Springer-Verlag, New York (2003)MATH
  
• 作者单位：Joseph Newhall (1)
  Robert K. Goodrich (2)
  
  1. Department of Mathematics and Statistics, Zayed University, Dubai, UAE
  2. University of Colorado, Boulder, CO, USA
  
• 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

This paper presents a generalization of the Arrow, Barankin and Blackwell theorem to locally convex Hausdorff topological vector spaces. Our main result relaxes the requirement that the objective set be compact; we show asymptotic compactness is sufficient, provided the asymptotic cone of the objective set can be separated from the ordering cone by a closed and convex cone. Additionally, we give a similar generalization using Henig efficient points when the objective set is not assumed to be convex. Our results generalize results of A. G?pfert, C. Tammer, and C. Z?linescu to locally convex spaces.