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

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.

Keywords:

• increasing positively homogeneous function
• min-type function
• unit simplex

2000 AMS Subject Classifications :

• 49K30
• 52A01

Acknowledgements

This work is supported by Mersin University Scientific Research Projects Unit and Akdeniz University Scientific Research Projects Unit.