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Erscheinungsjahr: 
2022
Quellenangabe: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 81 [Issue:] 2 [Publisher:] Springer US [Place:] New York, NY [Year:] 2022 [Pages:] 369-395
Verlag: 
Springer US, New York, NY
Zusammenfassung: 
This paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and a damped semismooth Newton method. The outer proximal regularization yields a numerically stable method, and we interpret the proximal operator as the unconstrained minimization of the primal-dual proximal augmented Lagrangian function. This allows the inner Newton scheme to exploit sparse symmetric linear solvers and multi-rank factorization updates. Moreover, the linear systems are always solvable independently from the problem data and exact linesearch can be performed. The proposed method can handle degenerate problems, provides a mechanism for infeasibility detection, and can exploit warm starting, while requiring only convexity. We present details of our open-source C implementation and report on numerical results against state-of-the-art solvers. QPDO proves to be a simple, robust, and efficient numerical method for convex quadratic programming.
Schlagwörter: 
Semismooth Newton method
Proximal point method
Regularized primal-dual method
Convex quadratic programming
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