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Trajectory-following methods for large-scale degenerate convex quadratic programming

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Abstract

We consider a class of infeasible, path-following methods for convex quadratric programming. Our methods are designed to be effective for solving both nondegerate and degenerate problems, where degeneracy is understood to mean the failure of strict complementarity at a solution. Global convergence and a polynomial bound on the number of iterations required is given. An implementation, CQP, is available as part of GALAHAD. We illustrate the advantages of our approach on the CUTEr and Maros–Meszaros test sets.

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Notes

  1. Available from http://galahad.rl.ac.uk/galahad-www/. A Matlab interface is also provided.

  2. When \(\ell \le 2\), the exact line minimizer of \(\phi \big (v_{k,\ell }(\alpha );\tau \big )\) is found by calculus.

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Acknowledgments

This work was supported by the EPSRC grants EP/E053351/1, EP/F005369/1 and EP/H026053/1 and NSERC Discovery Grant 299010-04. We are extremely grateful to a referee and associate editor for comments that lead to important clarifications of our numerical results.

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Authors and Affiliations

  1. Scientific Computing Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, UK

    Nicholas I. M. Gould

  2. GERAD and Mathematics and Industrial Engineering Department, École Polytechnique de Montréal, C. P. 6079, Succ. Centre Ville, Montreal, QC, H3C 3A7, Canada

    Dominique Orban

  3. Department of Applied Mathematics and Statistics, Johns Hopkins University, 100 Whitehead Hall, 3400 N. Charles Street, Baltimore, MD, 21218, USA

    Daniel P. Robinson

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  1. Nicholas I. M. Gould
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Correspondence to Nicholas I. M. Gould.

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Gould, N.I.M., Orban, D. & Robinson, D.P. Trajectory-following methods for large-scale degenerate convex quadratic programming. Math. Prog. Comp. 5, 113–142 (2013). https://doi.org/10.1007/s12532-012-0050-3

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