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A constraint-reduced MPC algorithm for convex quadratic programming, with a modified active set identification scheme

Author

Listed:
  • M. Paul Laiu

    (Oak Ridge National Laboratory)

  • André L. Tits

    (University of Maryland)

Abstract

A constraint-reduced Mehrotra-predictor-corrector algorithm for convex quadratic programming is proposed. (At each iteration, such algorithms use only a subset of the inequality constraints in constructing the search direction, resulting in CPU savings.) The proposed algorithm makes use of a regularization scheme to cater to cases where the reduced constraint matrix is rank deficient. Global and local convergence properties are established under arbitrary working-set selection rules subject to satisfaction of a general condition. A modified active-set identification scheme that fulfills this condition is introduced. Numerical tests show great promise for the proposed algorithm, in particular for its active-set identification scheme. While the focus of the present paper is on dense systems, application of the main ideas to large sparse systems is briefly discussed.

Suggested Citation

  • M. Paul Laiu & André L. Tits, 2019. "A constraint-reduced MPC algorithm for convex quadratic programming, with a modified active set identification scheme," Computational Optimization and Applications, Springer, vol. 72(3), pages 727-768, April.
    • Handle: RePEc:spr:coopap:v:72:y:2019:i:3:d:10.1007_s10589-019-00058-0
    DOI: 10.1007/s10589-019-00058-0
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    References listed on IDEAS

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    1. Luke B. Winternitz & André L. Tits & P.-A. Absil, 2014. "Addressing Rank Degeneracy in Constraint-Reduced Interior-Point Methods for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 127-157, January.
    2. Coralia Cartis & Yiming Yan, 2016. "Active-set prediction for interior point methods using controlled perturbations," Computational Optimization and Applications, Springer, vol. 63(3), pages 639-684, April.
    3. Sungwoo Park & Dianne P. O’Leary, 2015. "A Polynomial Time Constraint-Reduced Algorithm for Semidefinite Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 558-571, August.
    4. Sungwoo Park, 2016. "A Constraint-Reduced Algorithm for Semidefinite Optimization Problems with Superlinear Convergence," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 512-527, August.
    5. L. M. Graña Drummond & B. F. Svaiter, 1999. "On Well Definedness of the Central Path," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 223-237, August.
    6. Jin Jung & Dianne O’Leary & André Tits, 2012. "Adaptive constraint reduction for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 51(1), pages 125-157, January.
    7. Coralia Cartis & Yiming Yan, 2016. "Active-set prediction for interior point methods using controlled perturbations," Computational Optimization and Applications, Springer, vol. 63(3), pages 639-684, April.
    Full references (including those not matched with items on IDEAS)

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