A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Ruth Misener and Christodoulos A. Floudas ()
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Ruth Misener: Princeton University
Christodoulos A. Floudas: Princeton University

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 3, No 14, 905-932

Abstract: Abstract Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi: 10.1007/s10898-012-9874-7 ), 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.

Keywords: Mixed-integer signomial optimization; Global optimization; Numerical optimization software (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0396-3

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