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# GloMIQO: Global mixed-integer quadratic optimizer

## Author

Listed:
• Ruth Misener
• Christodoulos Floudas

()

## Abstract

This paper introduces the global mixed-integer quadratic optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to $${\varepsilon}$$ -global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the search space, bounding the variables, and finding good feasible solutions. To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure. The test cases are taken from process networks applications, computational geometry problems, GLOBALLib, MINLPLib, and the Bonmin test set. We compare the performance of GloMIQO with respect to four state-of-the-art global optimization solvers: BARON 10.1.2, Couenne 0.4, LindoGLOBAL 6.1.1.588, and SCIP 2.1.0. Copyright Springer Science+Business Media, LLC. 2013

## Suggested Citation

• Ruth Misener & Christodoulos Floudas, 2013. "GloMIQO: Global mixed-integer quadratic optimizer," Journal of Global Optimization, Springer, vol. 57(1), pages 3-50, September.
• Handle: RePEc:spr:jglopt:v:57:y:2013:i:1:p:3-50
DOI: 10.1007/s10898-012-9874-7
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File URL: http://hdl.handle.net/10.1007/s10898-012-9874-7
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## References listed on IDEAS

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1. Maranas, C. D. & Androulakis, I. P. & Floudas, C. A. & Berger, A. J. & Mulvey, J. M., 1997. "Solving long-term financial planning problems via global optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1405-1425, June.
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## Citations

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Cited by:

1. Frank, Stephen M. & Rebennack, Steffen, 2015. "Optimal design of mixed AC–DC distribution systems for commercial buildings: A Nonconvex Generalized Benders Decomposition approach," European Journal of Operational Research, Elsevier, vol. 242(3), pages 710-729.
2. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.
3. Santi, Éverton & Aloise, Daniel & Blanchard, Simon J., 2016. "A model for clustering data from heterogeneous dissimilarities," European Journal of Operational Research, Elsevier, vol. 253(3), pages 659-672.

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