IPRQP: a primal-dual interior-point relaxation algorithm for convex quadratic programming

We propose IPRQP, an enhanced primal-dual interior-point relaxation method (IPRM), for solving convex quadratic programming. This method is based on a smoothing barrier augmented Lagrangian function for convex quadratic programming. IPRQP inherits the advantages of IPRM, including not requiring iter...

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Bibliographic Details
Published in:Journal of global optimization 2023-11, Vol.87 (2-4), p.1027-1053
Main Authors: Zhang, Rui-Jin, Liu, Xin-Wei, Dai, Yu-Hong
Format: Article
Language:English
Subjects:
Algorithms
Comparative analysis
Computer Science
Investment analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
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Summary:We propose IPRQP, an enhanced primal-dual interior-point relaxation method (IPRM), for solving convex quadratic programming. This method is based on a smoothing barrier augmented Lagrangian function for convex quadratic programming. IPRQP inherits the advantages of IPRM, including not requiring iterative points to be interior points, which makes IPRQP suitable for the warm-starting of combinatorial optimization problems. Compared to IPRM, the customized starting points allow the line search of IPRQP to contain only vector operations. In addition, IPRQP improves the updating scheme of the barrier parameter and provides a certificate of infeasibility. Some results on global convergence are presented. We implement the algorithm on convex quadratic programming problems from Maros-Mészaros and the benchmark problem sets NETLIB and Kennington, which contain feasible and infeasible linear programming problems. The numerical results show that our algorithm is reliable for feasible problems and efficient for detecting the infeasibility of infeasible problems.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-023-01314-8