On constructing total orders and solving vector optimization problems with total orders

Kucuk M., Soyertem M., KÜÇÜK Y.

JOURNAL OF GLOBAL OPTIMIZATION, vol.50, no.2, pp.235-247, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.1007/s10898-010-9576-y
  • Journal Name: JOURNAL OF GLOBAL OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.235-247
  • Keywords: Nonconvex analysis, Vector optimization, Total order, Nonconvex optimization, Scalarization
  • Anadolu University Affiliated: Yes

Abstract

In this paper, we introduce a construction method of total ordering cone on R(n). It is shown that any total ordering cone on Rn is isomorphic to the cone R(lex)(n). Existence of a total ordering cone that contain given cone with a compact base is shown. By using this cone, a solving method of vector and set valued optimization problems is presented.