# 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} }

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…

## 21 Citations

### An Interior Point-Proximal Method of Multipliers for Linear Positive Semi-Definite Programming

- Mathematics, Computer ScienceJ. 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.

### An Interior Point-Proximal Method of Multipliers for Positive Semi-Definite Programming

- 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…

### A New Preconditioning Approachfor an Interior Point–Proximal Method of Multipliers for Linear and Convex Quadratic Programming

- 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.

### Proximal stabilized Interior Point Methods for quadratic programming and low-frequency-updates preconditioning techniques

- Computer Science, MathematicsArXiv
- 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.

### On a primal-dual Newton proximal method for convex quadratic programs

- Computer Science, MathematicsComputational 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.

### On a primal-dual Newton proximal method for convex quadratic programs

- Computer Science, MathematicsComput. 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.

### A new preconditioning approach for an interior point‐proximal method of multipliers for linear and convex quadratic programming

- Computer Science, MathematicsNumer. 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.

### A semismooth Newton-proximal method of multipliers for 𝓁1-regularized convex quadratic programming

- Computer Science, MathematicsArXiv
- 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.

### An active-set method for sparse approximations. Part I: Separable $\ell_1$ terms

- 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).

### Efficient Preconditioners for Interior Point Methods via a New Schur Complement-Based Strategy

- Computer ScienceSIAM 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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