A Framework for Globally Optimizing Mixed-Integer Signomial Programs

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

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Article ID: iaor2014746
Volume: 161
Issue: 3
Start Page Number: 905
End Page Number: 932
Publication Date: Jun 2014
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: global optimization, mixed integer programming, algebraic optimization
Abstract:

Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener and Floudas, 2012), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ϵ-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers.

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