Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (3): 581-592.

• Articles • Previous Articles     Next Articles

Monotone Minkowski Functionals and Scalarizations of Henig Proper Efficiency

 ZHANG Shen-Yuan1, QIU Jing-Hui2*   

  1. 1.School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090;
    2.School of Mathematical Sciences, Soochow University, Jiangsu Suzhou 215006
  • Received:2012-08-09 Revised:2013-03-11 Online:2014-06-25 Published:2014-06-25
  • Contact: QIU Jing-Hui,jhqiu@suda.edu.cn E-mail:jhqiu@suda.edu.cn
  • Supported by:

    国家自然科学基金(10871141)资助

Abstract:

Without the closedness and the pointedness of convex cones, we consider monotone Minkowski functionals generated
by general convex cones and investigate  properties of those Minkowski functionals. From this, in the framework of partially ordered locally convex spaces we obtain scalarizations of weakly efficient points of a general set and of a cone-bounded set by using a monotone continuous Minkowski functional and a monotone continuous semi-norm,
respectively.  Using the scalarizations of weak efficiency, we deduce scalarizations of Henig properly efficient points of a
general set and of a cone-bounded set, respectively. Moreover, when the ordering cone has a bounded base, we obtain some scalarization results on superefficiency in locally convex spaces. Finally we give some density results for Henig proper efficiency and superefficiency. These results generalize and improve the related known results.

Key words: Locally convex space, Minkowski functional, Weak efficiency, Henig proper efficiency, Scalarization, Density

CLC Number: 

  • 90C29
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