A First-Order Numerical Algorithm without Matrix Operations

Muhammad Adil; Ramtin Madani; Sasan Tavakkol; Ali Davoudi

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arXiv · 2203.05027

A First-Order Numerical Algorithm without Matrix Operations

Muhammad Adil·Ramtin Madani·Sasan Tavakkol·Ali Davoudi

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Abstract

This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical algorithms. Existing direct and indirect methods are either computationally expensive or compromise on solution accuracy. Alternatively, we propose an easy-to-compute decomposition method to solve sparse linear systems that arise in conic optimization problems. Its iterations are tractable, highly parallelizable, with closed-form solutions. This algorithm can be easily implemented on distributed platforms, such as graphics processing units, with orders-of-magnitude time improvement. The performance of the proposed solver is demonstrated on large-scale conic optimization problems and is compared with the state-of-the-art first-order solvers.

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Muhammad Adil, Ramtin Madani, Sasan Tavakkol, Ali Davoudi. 2022-03-09. A First-Order Numerical Algorithm without Matrix Operations. https://arxiv.org/abs/2203.05027

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