A reformulation framework for global optimization

Andreas Lundell (), Anders Skjäl and Tapio Westerlund

Journal of Global Optimization, 2013, vol. 57, issue 1, 115-141

Abstract: In this paper, we present a global optimization method for solving nonconvex mixed integer nonlinear programming (MINLP) problems. A convex overestimation of the feasible region is obtained by replacing the nonconvex constraint functions with convex underestimators. For signomial functions single-variable power and exponential transformations are used to obtain the convex underestimators. For more general nonconvex functions two versions of the so-called αBB-underestimator, valid for twice-differentiable functions, are integrated in the actual reformulation framework. However, in contrast to what is done in branch-and-bound type algorithms, no direct branching is performed in the actual algorithm. Instead a piecewise convex reformulation is used to convexify the entire problem in an extended variable-space, and the reformulated problem is then solved by a convex MINLP solver. As the piecewise linear approximations are made finer, the solution to the convexified and overestimated problem will form a converging sequence towards a global optimal solution. The result is an easily-implementable algorithm for solving a very general class of optimization problems. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Global optimization; Reformulation technique; Convex underestimators; Mixed integer nonlinear programming; Twice-differentiable functions; Signomial functions; Piecewise linear functions; αBB-underestimator; SGO-algorithm (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10898-012-9877-4

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