Table 1 Comparison of Algorithm 1 (IA) with the algorithm without inertia step (UA) for Example 4.1. \(x_{0}=\operatorname{randn}(N,1)\)
From: New inertial proximal gradient methods for unconstrained convex optimization problems
ϵ | IA | UA | ||||||
|---|---|---|---|---|---|---|---|---|
n | t | \(\Vert x_{n+1}-x_{n}\Vert \) | \(\Vert Ax_{n}-b\Vert \) | n | t | \(\Vert x_{n+1}-x_{n}\Vert \) | \(\Vert Ax_{n}-b\Vert \) | |
10−3 | 143 | 0.0546 | 7.8635 × 10−7 | 7.9601 | 685 | 0.4510 | 9.8753 × 10−4 | 8.7650 |
10−5 | 636 | 0.8414 | 6.6975 × 10−8 | 2.8313 | 5768 | 3.8915 | 9.2786 × 10−5 | 3.6433 |
10−7 | 1391 | 1.0010 | 8.3482 × 10−9 | 0.8189 | 14,768 | 6.0098 | 9.9947 × 10−8 | 1.3663 |
10−9 | 2023 | 1.0035 | 1.7182 × 10−12 | 0.1473 | 56,077 | 7.0788 | 9.9989 × 10−10 | 0.5936 |