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A computational study of global optimization solvers on two trust region subproblems

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  • Tiago Montanher

    (University of Vienna)

  • Arnold Neumaier

    (University of Vienna)

  • Ferenc Domes

    (University of Vienna)

Abstract

One of the relevant research topics to which Chris Floudas contributed was quadratically constrained quadratic programming (QCQP). This paper considers one of the simplest hard cases of QCQP, the two trust region subproblem (TTRS). In this case, one needs to minimize a quadratic function constrained by the intersection of two ellipsoids. The Lagrangian dual of the TTRS is a semidefinite program (SDP) and this result has been extensively used to solve the problem efficiently. We focus on numerical aspects of branch-and-bound solvers with three goals in mind. We provide (i) a detailed analysis of the ability of state-of-the-art solvers to complete the global search for a solution, (ii) a quantitative approach for measuring the cluster effect on each solver and (iii) a comparison between the branch-and-bound and the SDP approaches. We perform the numerical experiments on a set of 212 challenging problems provided by Kurt Anstreicher. Our findings indicate that SDP relaxations and branch-and-bound have orthogonal difficulties, thus pointing to a possible benefit of a combined method. The following solvers were selected for the experiments: Antigone 1.1, Baron 16.12.7, Lindo Global 10.0, Couenne 0.5 and SCIP 3.2.

Suggested Citation

  • Tiago Montanher & Arnold Neumaier & Ferenc Domes, 2018. "A computational study of global optimization solvers on two trust region subproblems," Journal of Global Optimization, Springer, vol. 71(4), pages 915-934, August.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:4:d:10.1007_s10898-018-0649-7
    DOI: 10.1007/s10898-018-0649-7
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    References listed on IDEAS

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    1. Hermann Schichl & Mihály Markót & Arnold Neumaier, 2014. "Exclusion regions for optimization problems," Journal of Global Optimization, Springer, vol. 59(2), pages 569-595, July.
    2. Alexandre Goldsztejn & Ferenc Domes & Brice Chevalier, 2014. "First order rejection tests for multiple-objective optimization," Journal of Global Optimization, Springer, vol. 58(4), pages 653-672, April.
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    Cited by:

    1. Nadav Hallak & Marc Teboulle, 2020. "Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 480-503, August.

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