# An interior point-proximal method of multipliers for convex quadratic programming

@article{Pougkakiotis2019AnIP,
title={An interior point-proximal method of multipliers for convex quadratic programming},
author={Spyridon Pougkakiotis and Jacek Gondzio},
journal={Computational Optimization and Applications},
year={2019},
volume={78},
pages={307 - 351}
}
• Published 23 April 2019
• Computer Science, Mathematics
• Computational Optimization and Applications
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained convex quadratic programming problems. We apply few iterations of the interior point method to each sub-problem of the proximal method of multipliers. Once a satisfactory solution of the PMM sub-problem is found, we update the PMM parameters, form a new IPM…
• Mathematics, Computer Science
J. Optim. Theory Appl.
• 2022
This paper combines an infeasible Interior Point Method with the Proximal Method of Multipliers and interpret the algorithm (IP-PMM) as a primal-dual regularized IPM, suitable for solving SDP problems, and proves polynomial complexity of the algorithm.
• Mathematics, Computer Science
• 2020
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM) and interpret the algorithm (IP-PMM) as a primal-dual regularized IPM, suitable for
• Computer Science, Mathematics
• 2020
A novel preconditioning strategy is proposed which is based on a suitable sparsiﬁcation of the normal equations matrix in the linear case, and also con-stitutes the foundation of a block-diagonal preconditionser to accelerate MINRES for linear systems arising from the solution of general quadratic programming problems.
• Computer Science, Mathematics
ArXiv
• 2022
This work interprets Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the framework of the Proximal Point Method, and proposes general purpose preconditioners which, exploiting the regularization and a new rearrangement of the Schur complement, remain attractive for a series of subsequent IPM iterations.
• Alberto De Marchi
• Computer Science, Mathematics
Computational Optimization and Applications
• 2022
QPDO is introduced, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and a damped semismooth Newton method, and proves to be a simple, robust, and efficient numerical method.
• A. Marchi
• Computer Science, Mathematics
Comput. Optim. Appl.
• 2022
QPDO is introduced, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and a damped semismooth Newton method, and proves to be a simple, robust, and efficient numerical method.
• Computer Science, Mathematics
Numer. Linear Algebra Appl.
• 2021
A novel preconditioning strategy is proposed which is based on a suitable sparsification of the normal equations matrix in the linear case, and also constitutes the foundation of a block‐diagonal preconditionser to accelerate MINRES for linear systems arising from the solution of general quadratic programming problems.
• Computer Science, Mathematics
ArXiv
• 2022
This paper shows that the method derived by suitably combining a proximal method of multipliers strategy with a semi-smooth Newton method achieves global convergence under feasibility assumptions and can achieve global linear and local superlinear convergence.
• Computer Science
• 2022
An active-set method for the solution of $\ell_1$-regularized convex quadratic optimization problems derived by combining a proximal method of multipliers (PMM) strategy with a standard semismooth Newton method (SSN).
• Computer Science
SIAM J. Matrix Anal. Appl.
• 2022
Numerical experiments with synthetic problems and problems from the Maros-Mészáros QP collection show that the preconditioned inexact interior point solvers are effective at improving conditioning and reducing cost.

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