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A framework for globally optimizing mixed-integer signomial programs. (English) Zbl 1303.90074
Summary: Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO [R. Misener and C. A. Floudas, J. Glob. Optim. 57, No. 1, 3–50 (2013; Zbl 1272.90034)], this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to \(\varepsilon\)-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.

MSC:
90C11 Mixed integer programming
90C26 Nonconvex programming, global optimization
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