On the minimization of a class of generalized linear functions on a flow polytope

Abstract

The aim of this paper is to propose a solution method for the minimization of a class of generalized linear functions on a flow polytope. The problems will be solved by means of a network algorithm, based on graph operations, which lies within the class of the so-called ‘optimal level solutions’ parametric methods. The use of the network structure of flow polytopes, allows to obtain good algorithm performances and small numerical errors. Results of a computational test are also provided.

Keywords:

• network flows
• nonconvex programming
• global optimization
• optimal level solutions

AMS Subject Classifications:

• 90C35
• 90C26
• 90C31