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Optimal iterative QP and QPQC algorithms

Author

Listed:
  • Zdeněk Dostál

    (Technical University of Ostrava)

  • Lukáš Pospíšil

    (Technical University of Ostrava)

Abstract

We review our recent results in the development of optimal algorithms for the minimization of a strictly convex quadratic function subject to separable convex inequality constraints and/or linear equality constraints. A unique feature of our algorithms is the theoretically supported bound on the rate of convergence in terms of the bounds on the spectrum of the Hessian of the cost function, independent of representation of the constraints. When applied to the class of convex QP or QPQC problems with the spectrum in a given positive interval and a sparse Hessian matrix, the algorithms enjoy optimal complexity, i.e., they can find an approximate solution at the cost that is proportional to the number of unknowns. The algorithms do not assume representation of the linear equality constraints by full rank matrices. The efficiency of our algorithms is demonstrated by the evaluation of the projection of a point to the intersection of the unit cube and unit sphere with hyperplanes.

Suggested Citation

  • Zdeněk Dostál & Lukáš Pospíšil, 2016. "Optimal iterative QP and QPQC algorithms," Annals of Operations Research, Springer, vol. 243(1), pages 5-18, August.
    • Handle: RePEc:spr:annopr:v:243:y:2016:i:1:d:10.1007_s10479-013-1479-0
    DOI: 10.1007/s10479-013-1479-0
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    References listed on IDEAS

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    1. Jacek Gondzio & Andreas Grothey, 2007. "Parallel interior-point solver for structured quadratic programs: Application to financial planning problems," Annals of Operations Research, Springer, vol. 152(1), pages 319-339, July.
    2. L. Fernandes & A. Fischer & J. Júdice & C. Requejo & J. Soares, 1998. "A block active set algorithm for large-scalequadratic programming with box constraints," Annals of Operations Research, Springer, vol. 81(0), pages 75-96, June.
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