Table 2 Comparison of Algorithm 3 (AIA) with Algorithm 1 (IA) for Example 4.2. \(u=e^{t}\), \(x_{0}=t\), \(x_{1}=t^{2}\)
From: New inertial proximal gradient methods for unconstrained convex optimization problems
ϵ | AIA | IA | ||||||
|---|---|---|---|---|---|---|---|---|
n | t | \(\Vert x_{n+1}-x_{n}\Vert \) | \(\Vert x_{n}\Vert \) | n | t | \(\Vert x_{n+1}-x_{n}\Vert \) | \(\Vert x_{n}\Vert \) | |
10−3 | 17 | 0.0007 | 9.0023 × 10−4 | 1.0001 | 21 | 0.0011 | 9.0302 × 10−4 | 1.0001 |
10−7 | 101 | 0.0025 | 9.9998 × 10−8 | 1.0000 | 132 | 0.0034 | 9.9989 × 10−8 | 1.0000 |
10−8 | 316 | 0.0063 | 8.3482 × 10−9 | 1.0000 | 715 | 0.0072 | 9.9947 × 10−8 | 1.0000 |
10−9 | 996 | 0.0206 | 1.7182 × 10−12 | 1.0000 | 1087 | 0.0317 | 9.9989 × 10−10 | 1.0000 |