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Numerical Methods for Large-Scale Non-Convex Quadratic Programming

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Trends in Industrial and Applied Mathematics

Part of the book series: Applied Optimization ((APOP,volume 72))

Abstract

We consider numerical methods for finding (weak) second-order critical points for large-scale non-convex quadratic programming problems. We describe two new methods. The first is of the active-set variety. Although convergent from any starting point, it is intended primarily for the case where a good estimate of the optimal active set can be predicted. The second is an interior-point trust-region type, and has proved capable of solving problems involving up to half a million unknowns and constraints. The solution of a key equality constrained subproblem, common to both methods, is described. The results of comparative tests on a large set of convex and non-convex quadratic programming examples are given.

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Author information

Authors and Affiliations

  1. Computational Science and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England

    Nicholas I. M. Gould

  2. Department of Mathematics, FUNDP, Rempart de la Vierge, 8, B-5000, Namur, Belgium

    Philippe L. Toint

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  1. Nicholas I. M. Gould
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  2. Philippe L. Toint
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Editors and Affiliations

  1. Department of Mathematical Sciences, King Fand University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Abul Hasan Siddiqi

  2. Institute of Applied Mathematics, University of Erlangen, Erlangen, Germany

    Michal Kočvara

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© 2002 Kluwer Academic Publishers

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Gould, N.I.M., Toint, P.L. (2002). Numerical Methods for Large-Scale Non-Convex Quadratic Programming. In: Siddiqi, A.H., Kočvara, M. (eds) Trends in Industrial and Applied Mathematics. Applied Optimization, vol 72. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0263-6_8

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  • DOI: https://doi.org/10.1007/978-1-4613-0263-6_8

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  • Online ISBN: 978-1-4613-0263-6

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