Global optimization of MINLP problems containing signomial functions

Wednesday, November 19, 2008 - 10:30am - 11:15am
EE/CS 3-180
Tapio Westerlund (Åbo Akademi (Finland-Swedish University of Åbo))
Joint work with Andreas Lundell,
Process Design and Systems Engineering, Åbo Akademi University
Biskopsgatan 8, FIN-20500 Turku, Finland.

Keywords: Transformation techniques; mixed integer nonlinear programming; signomial functions; global optimization.

In this presentation some transformation techniques are discussed. With the given techniques a class of non-convex MINLP problems, including signomial functions, can be solved to global optimality. The transformation techniques are based on single variable power and exponential transformations and the signomial functions can be converted into convex form, by the transformations. In addition, the original non-convex problem can be relaxed into convex form, if the transformations have certain properties and the inverse transformations are approximated by piecewise linear functions.

The transformations are not unique and there exists degrees of freedom in selecting them. For determining an optimal set of transformations a mixed integer linear programming (MILP) problem can be formulated. The solution of the MILP problem can be used separately but acts, in our case, as a pre-processing step in the global optimization framework. Certain properties of the transformations can be emphasized in the initial MILP pre-processing step. For example, the total number of transformations needed can be minimized. The principles behind the transformation techniques are given and some numerical examples are used to illustrate the given techniques.
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