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

M. Paul Laiu () and André L. Tits ()
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M. Paul Laiu: Oak Ridge National Laboratory
André L. Tits: University of Maryland

Computational Optimization and Applications, 2019, vol. 72, issue 3, No 8, 727-768

Abstract: 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.

Keywords: Convex quadratic programming; Constraint reduction; Primal-dual interior-point method; Mehrotra’s predictor-corrector; Regularization; Active constraints identification (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10589-019-00058-0

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