Existence and characterization theorems in nonconvex vector optimization


Journal of Global Optimization, vol.62, no.1, pp.155-165, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.1007/s10898-014-0234-7
  • Journal Name: Journal of Global Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.155-165
  • Keywords: Vector optimization, Nonlinear separation theorem, Augmented dual cone, Sublinear scalarizing functions, Conic scalarization method, Proper efficiency, Existence theorem, EFFICIENT POINTS, PORTFOLIO OPTIMIZATION, RADIAL EPIDERIVATIVES, PROPER EFFICIENCY, SCALARIZATION, PREFERENCES, ASSIGNMENT, SEPARATION, DUALITY, BISHOP
  • Anadolu University Affiliated: Yes


© 2014, Springer Science+Business Media New York.This paper presents existence conditions and characterization theorems for minimal points of nonconvex vector optimization problems in reflexive Banach spaces. Characterization theorems use special class of monotonically increasing sublinear scalarizing functions which are defined by means of elements of augmented dual cones. It is shown that the Hartley cone-compactness is necessary and sufficient to guarantee the existence of a properly minimal point of the problem. The necessity is proven in the case of finite dimensional space.