Основні поняття
Efficiently solving large-scale SDPs with HALLaR method.
Анотація
The paper introduces HALLaR, a first-order method for solving large-scale semidefinite programs with bounded domain. It utilizes a hybrid low-rank approach to find near-optimal solutions efficiently. HALLaR outperforms state-of-the-art solvers in terms of accuracy and computational time, especially in applications like maximum stable set, phase retrieval, and matrix completion. The method combines an inexact augmented Lagrangian approach with Frank-Wolfe steps to escape local stationary points and find global solutions.
Статистика
In less than 20 minutes, HALLaR can solve a maximum stable set SDP instance with dimension pair (n, m) ≈ (106, 107) within 10^-5 relative precision.
HALLaR takes approximately 1.75 hours on a personal laptop to solve within 10^-5 relative precision maximum stable set SDP instance for a Hamming graph with n ≈ 4,000,000 and m ≈ 40,000,000.
HALLaR takes approximately 7.5 hours on a personal laptop to solve within 10^-5 relative precision a phase retrieval SDP instance with n = 1,000,000 and m = 12,000,000.
Цитати
"HALLaR finds highly accurate solutions in substantially less CPU time than other solvers."
"HALLaR utilizes an adaptive proximal point method combined with Frank-Wolfe steps for efficient solution finding."