TY - JOUR
T1 - A constraint-reduced MPC algorithm for convex quadratic programming, with amodified active set identification scheme
AU - Laiu, M. Paul
AU - Tits, André L.
N1 - Publisher Copyright:
© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2019.
PY - 2019/4
Y1 - 2019/4
N2 - 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.
AB - 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.
KW - Active constraints identification
KW - Constraint reduction
KW - Convex quadratic programming
KW - Mehrotra’s predictor-corrector
KW - Primal-dual interior-point method
KW - Regularization
UR - http://www.scopus.com/inward/record.url?scp=85062718100&partnerID=8YFLogxK
U2 - 10.1007/s10589-019-00058-0
DO - 10.1007/s10589-019-00058-0
M3 - Article
AN - SCOPUS:85062718100
SN - 0926-6003
VL - 72
SP - 727
EP - 768
JO - Computational Optimization and Applications
JF - Computational Optimization and Applications
IS - 3
ER -