Some convexifications in global optimization of problems containing signomial terms

It is often possible to use different convexification techniques with different transformations in global optimization. In 'Optimization Eng. (submitted for publication)', a new global optimization technique based on convexifying signomial terms is presented. The technique is based on the solution of a sequence of convexified approximate subproblems. The choice of transformation functions is clearly essential. It is not enough to use convexifications that will result in convex and underestimating problems, if an effective optimization approach is wanted. The transformations should be such that they make the resulting problems convex but at the same time do not change the problem more than necessary. It will be shown in this article that for certain problems the choice of transformations has a clear influence on the efficiency of the proposed optimization approach. Using other transformations than what is proposed in 'Optimization Eng. (submitted for publication)' will, in some examples, give solution times that are shorter by an order of magnitude. The concept of power convex functions (Generalized Concavity Optimization Econ. (1981) 153) will be used as a measure of the quality of the transformations. In this paper, the new transformation functions are also shown to be very successful in a heat exchanger network synthesis application. (C) 2002 Elsevier Science Ltd. All rights reserved.