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… 
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21 Citations

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

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

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  • Computer Science, Mathematics
    Comput. Optim. Appl.
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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

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.

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