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

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.

Authors:
ORCiD logo [1]; ORCiD logo [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
  2. Univ. of Maryland, College Park, MD (United States). Dept. of Electrical and Computer Engineering & Institute for Systems Research
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1559748
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Computational Optimization and applications
Additional Journal Information:
Journal Volume: 72; Journal Issue: 3; Journal ID: ISSN 0926-6003
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Convex quadratic programming; Constraint reduction; Primal-dual interior-point method; Mehrotra’s predictor-corrector; Regularization; Active constraints identification

Citation Formats

Laiu, M. Paul, and Tits, André L. A constraint-reduced MPC algorithm for convex quadratic programming, with a modified active set identification scheme. United States: N. p., 2019. Web. doi:10.1007/s10589-019-00058-0.
Laiu, M. Paul, & Tits, André L. A constraint-reduced MPC algorithm for convex quadratic programming, with a modified active set identification scheme. United States. doi:10.1007/s10589-019-00058-0.
Laiu, M. Paul, and Tits, André L. Sat . "A constraint-reduced MPC algorithm for convex quadratic programming, with a modified active set identification scheme". United States. doi:10.1007/s10589-019-00058-0.
@article{osti_1559748,
title = {A constraint-reduced MPC algorithm for convex quadratic programming, with a modified active set identification scheme},
author = {Laiu, M. Paul and Tits, André L.},
abstractNote = {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.},
doi = {10.1007/s10589-019-00058-0},
journal = {Computational Optimization and applications},
number = 3,
volume = 72,
place = {United States},
year = {2019},
month = {3}
}

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