# Global optimization of signomial programming problems

B3 Non-refereed conference proceedings

Internal Authors/Editors

Publication Details

List of Authors: Tapio Westerlund, Andreas Lundell

Editors: Pierre Bonami, Leo Liberti, Andrew J. Miller, Annick Sartenaer

Place: Marseille

Publication year: 2010

Publisher: CIRM

Book title: Proceedings of the European Workshop on Mixed Integer Nonlinear Programming

Start page: 89

End page: 92

Abstract

In this presentation, an overview of a signomial global optimization algorithm is given. As the name indicates, the algorithm can be used to solve mixed integer nonlinear programming problems containing signomial functions to global optimality. The method employs singlevariable power and exponential transformations for convexifying the nonconvex signomial functions termwise. By approximating the transformations using piecewise linear functions, piecewise convex underestimators for the nonconvex signomial functions as well as a relaxed convex problem can be obtained. In the algorithm, the approximations resulting from the piecewise linear functions are subsequentially improved resulting in a set of subproblems whose optimal solution converges to that of the original nonconvex problem. Finally, some recent theoretical results regarding the underestimation properties of the convexified signomial terms obtained using different transformations are also given