Exponential and Power Transformations for Convexifying Signomial Terms in MINLP Problems

A. Lundell and T. Westerlund (Finland)

Keywords

MINLP, signomial functions, convexification, power trans formation, exponential transformation, bilinear terms.

Abstract

In MINLP (mixed integer nonlinear programming) prob lems, signomial functions – especially functions containing biand trilinear terms – are quite common. Problems of this type are generally nonconvex, but it has been shown that it is always possible to write them in a convex form using a two-step transformation technique: In the first step, the sig nomial terms in the problem are convexified using transfor mations on the individual variables, and in the second step, the transformations are approximated with piecewise linear functions so that the feasible region of the original problem is overestimated. Valid transformations are, for example, power and exponential transformations. However, there exists some degrees of freedom re garding how the transformations can be chosen. In this pa per, a method is described for optimizing the set of transfor mations applied to the problem, by formulating and solving a MILP (mixed integer linear programming) problem. A variant of this method has been presented earlier for power transformations, but it is here extended to include exponen tial transformations as well. Finally, comparisons of the accuracy of the approxi mations with the convex envelope of bilinear terms are pro vided.

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