Convex underestimation strategies for signomial functions

Abstract

Different types of underestimation strategies are used in deterministic global optimization. In this paper, convexification and underestimation techniques applicable to problems containing signomial functions are studied. Especially, power transformation and exponential transformation (ET) will be considered in greater detail and some new theoretical results regarding the relation between the negative power transformation and the ET are given. The techniques are, furthermore, illustrated through examples and compared with other underestimating methods used in global optimization solvers such as αBB and BARON.

Keywords:

• signomial functions
• convex underestimators
• deterministic global optimization
• MINLP
• exponential transformation
• power transformation

AMS Subject Classification :

• 90C26
• 90C27
• 90C30

Acknowledgements

A.L. gratefully acknowledges financial support from the Research Institute of the Foundation of Åbo Akademi University.