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# 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:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
- 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}

}

*Citation information provided by*

Web of Science

Web of Science

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