Reformulations for utilizing separability when solving convex MINLP problems

A1 Journal article (refereed)


Internal Authors/Editors


Publication Details

List of Authors: Jan Kronqvist, Andreas Lundell, Tapio Westerlund
Publisher: SPRINGER
Publication year: 2018
Journal: Journal of Global Optimization
Journal acronym: J GLOBAL OPTIM
Volume number: 71
Issue number: 3
Start page: 571
End page: 592
Number of pages: 22
ISSN: 0925-5001


Abstract

Several deterministic methods for convex mixed integer nonlinear programming generate a polyhedral approximation of the feasible region, and utilize this approximation to obtain trial solutions. Such methods are, e.g., outer approximation, the extended cutting plane method and the extended supporting hyperplane method. In order to obtain the optimal solution and verify global optimality, these methods often require a quite accurate polyhedral approximation. In case the nonlinear functions are convex and separable to some extent, it is possible to obtain a tighter approximation by using a lifted polyhedral approximation, which can be achieved by reformulating the problem. We prove that under mild assumptions, it is possible to obtain tighter linear approximations for a type of functions referred to as almost additively separable. Here it is also shown that solvers, by a simple reformulation, can benefit from the tighter approximation, and a numerical comparison demonstrates the potential of the reformulation. The reformulation technique can also be combined with other known transformations to make it applicable to some nonseparable convex functions. By using a power transform and a logarithmic transform the reformulation technique can for example be applied to p-norms and some convex signomial functions, and the benefits of combining these transforms with the reformulation technique are illustrated with some numerical examples.


Keywords

Convex MINLP, extended cutting plane algorithm, Extended supporting hyperplane algorithm, Lifted polyhedral approximation, Outer approximation, Separable MINLP

Last updated on 2019-23-07 at 05:12

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