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Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations

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Abstract

We propose a deterministic global optimization approach, whose novel contributions are rooted in the edge-concave and piecewise-linear underestimators, to address nonconvex mixed-integer quadratically-constrained quadratic programs (MIQCQP) to \({\epsilon}\) -global optimality. The facets of low-dimensional (n ≤ 3) edge-concave aggregations dominating the termwise relaxation of MIQCQP are introduced at every node of a branch-and-bound tree. Concave multivariable terms and sparsely distributed bilinear terms that do not participate in connected edge-concave aggregations are addressed through piecewise-linear relaxations. Extensive computational studies are presented for point packing problems, standard and generalized pooling problems, and examples from GLOBALLib (Meeraus, Globallib. http://www.gamsworld.org/global/globallib.htm).

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  1. Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Ruth Misener & Christodoulos A. Floudas

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  1. Ruth Misener
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Correspondence to Christodoulos A. Floudas.

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The authors gratefully acknowledge support from the National Science Foundation (CBET–0827907).

R.M. is further thankful for her NSF Graduate Research Fellowship (DGE-0646086).

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Misener, R., Floudas, C.A. Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations. Math. Program. 136, 155–182 (2012). https://doi.org/10.1007/s10107-012-0555-6

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