Journal of Global Optimization

, Volume 57, Issue 1, pp 3–50 | Cite as

GloMIQO: Global mixed-integer quadratic optimizer

Article

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.

Keywords

Mixed-integer quadratically-constrained quadratic programs Numerical optimization software Mathematical programming reformulations Branch-and-bound global optimization 

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© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  1. 1.Department of Chemical and Biological EngineeringPrinceton UniversityPrincetonUSA

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