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arXiv · 2404.14524

Randomized Nystr\"om Preconditioned Interior Point-Proximal Method of Multipliers

Ya-Chi Chu·Luiz-Rafael Santos·Madeleine Udell
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Abstract

We present a new algorithm for convex separable quadratic programming (QP) called Nys-IP-PMM, a regularized interior-point solver that uses low-rank structure to accelerate solution of the Newton system. The algorithm combines the interior point proximal method of multipliers (IP-PMM) with the randomized Nystr\"om preconditioned conjugate gradient method as the inner linear system solver. Our algorithm is matrix-free: it accesses the input matrices solely through matrix-vector products, as opposed to methods involving matrix factorization. It works particularly well for separable QP instances with dense constraint matrices. We establish convergence of Nys-IP-PMM. Numerical experiments demonstrate its superior performance in terms of wallclock time compared to previous matrix-free IPM-based approaches.

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Ya-Chi Chu, Luiz-Rafael Santos, Madeleine Udell. 2024-04-22. Randomized Nystr\"om Preconditioned Interior Point-Proximal Method of Multipliers. https://arxiv.org/abs/2404.14524

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