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

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 regular...

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Published in:	Computational optimization and applications Vol. 72; no. 3; pp. 727 - 768
Main Authors:	Laiu, M. Paul, Tits, André L.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.04.2019 Springer Nature B.V Springer
Subjects:	Active constraints identification Algorithms Constraint reduction Convex and Discrete Geometry Convex quadratic programming Iterative methods Management Science Mathematics MATHEMATICS AND COMPUTING Mathematics and Statistics Mehrotra’s predictor-corrector Operations Research Operations Research/Decision Theory Optimization Predictor-corrector methods Primal-dual interior-point method Quadratic programming Regularization Statistics Convex quadratic programming Constraint reduction Primal-dual interior-point method Mehrotra’s predictor-corrector Regularization Active constraints identification
ISSN:	0926-6003, 1573-2894
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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.
AbstractList	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.
Author	Laiu, M. Paul Tits, André L.
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CitedBy_id	crossref_primary_10_1137_21M1413134 crossref_primary_10_1007_s10107_021_01692_5 crossref_primary_10_1016_j_isatra_2021_11_031 crossref_primary_10_1007_s12555_021_0901_7 crossref_primary_10_1137_18M1196297
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ContentType	Journal Article
Copyright	This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2019 Computational Optimization and Applications is a copyright of Springer, (2019). All Rights Reserved.
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Keywords	Convex quadratic programming Constraint reduction Primal-dual interior-point method Mehrotra’s predictor-corrector Regularization Active constraints identification
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Snippet	A constraint-reduced Mehrotra-predictor-corrector algorithm for convex quadratic programming is proposed. (At each iteration, such algorithms use only a subset...
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SubjectTerms	Active constraints identification Algorithms Constraint reduction Convex and Discrete Geometry Convex quadratic programming Iterative methods Management Science Mathematics MATHEMATICS AND COMPUTING Mathematics and Statistics Mehrotra’s predictor-corrector Operations Research Operations Research/Decision Theory Optimization Predictor-corrector methods Primal-dual interior-point method Quadratic programming Regularization Statistics
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Title	A constraint-reduced MPC algorithm for convex quadratic programming, with a modified active set identification scheme
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