Smoothing Approximation to the Square-Order Exact Penalty Functions for Constrained Optimization

Table 2

Numerical results for Example 1 by Algorithm 10.

𝑗	𝑥^∗𝑗	𝑞𝑗	𝜖𝑗	𝑔1(𝑥^∗𝑗)	𝑔2(𝑥^∗𝑗)	𝑓(𝑥^∗𝑗)
0	0.0039020.006869	0.1	10^−1	1.424453	1.668849	1.009072
1	0.37397300.7309830	0.1×5	10^−2	0.6182998	−2.001706	1.686692
2	0.39716050.7207292	0.1×5^2	10^−3	0.5285448	−1.937189	1.833846
3	0.72771280.3901970	0.1×5^3	10^−4	−0.7890318	0.050637	1.761504
4	0.72593670.3969422	0.1×5^4	10^−5	−0.7791997	0.012894	1.815956
5	0.72547780.3987666	0.1×5^5	10^−6	−0.7765785	0.002733	1.832846
6	0.72714510.3997456	0.1×5^6	10^−7	−0.7800440	0.000062	1.837930
7	0.72713370.3997256	0.1×5^7	10^−8	−0.7800310	0.000150	1.837770
8	0.72606960.3994698	0.1×5^8	10^−9	−0.7775255	−0.000066	1.837740