On the global minimization of increasing positively homogeneous functions over the unit simplex

Adilov G., TINAZTEPE G., Tınaztepe R.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.87, no.12, pp.2733-2746, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 87 Issue: 12
  • Publication Date: 2010
  • Doi Number: 10.1080/00207160902745341
  • Journal Name: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2733-2746
  • Keywords: increasing positively homogeneous function, min-type function, unit simplex, CUTTING ANGLE METHOD, OPTIMIZATION
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, the problem of finding the global minimum of increasing positively homogeneous functions (IPH) over the unit simplex is studied. As IPH functions are abstract convex with respect to min-type functions, cutting angle method is applied to this problem. In this method, the problem of minimization of IPH functions is reduced to a sequence of subproblems with simple max-min-type objective functions. In this work, we propose a new algorithm for solving the subproblem. This algorithm is different from other versions of the cutting angle algorithm in that it is based on a geometrical approach and it is simpler and faster than others.