Papers › Randomized Nyström Preconditioned Interior Point-Proximal Method of Multipliers
Randomized Nyström Preconditioned Interior Point-Proximal Method of Multipliers
Ya-Chi Chu, Luiz-Rafael Santos, Madeleine Udell
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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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