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Table 3 Comparison of Algorithm 3 (AIA) with Algorithm 1 (IA) for Example 4.2. \(u=\sin t\), \(x_{0}=t\), \(x_{1}=2t\)

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

127

0.0051

9.3714 × 10−4

1.0001

130

0.0053

9.7883 × 10−4

1.0001

10−5

525

0.0145

8.2615 × 10−6

1.0000

534

0.0182

9.1975 × 10−6

1.0000

10−7

1052

0.0299

9.4418 × 10−8

1.0000

1077

0.0343

9.8397 × 10−8

1.0000

10−8

2011

0.0611

9.9554 × 10−9

1.0000

2071

0.0697

9.9885 × 10−9

1.0000