General Ekeland's Variational Principle for Set-Valued Mappings

  • G. Y. Chen
  • X. X. Huang
  • S. H. Hou

Abstract

In this paper, we introduce the concept of approximate solutions for set-valued optimization problems. A sufficient condition for the existence of approximate solutions is obtained. A general Ekeland's variational principle for set-valued mappings in complete ordered metric spaces and complete metric spaces are derived. These results are generalizations of results for vector-valued functions in Refs. 1–4.

Set-valued optimization variational principle Hausdorff maximality principle 

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • G. Y. Chen
    • 1
  • X. X. Huang
    • 2
  • S. H. Hou
    • 3
  1. 1.Institute of Systems ScienceAcademia SinicaBeijingChina
  2. 2.Department of Mathematics and Computer ScienceChongqing Normal UniversityChongqingChina
  3. 3.Department of Applied MathematicsHong Kong Polytechnic UniversityHong Kong, China

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