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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
AC05-00OR22725
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-019-00058-0