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

Table 5

Numerical results for Example 2 by Algorithm 10.

𝑗	𝑥^∗𝑗	𝑞𝑗	𝜖𝑗	𝑔1(𝑥^∗𝑗)	𝑔2(𝑥^∗𝑗)	𝑔3(𝑥^∗𝑗)	𝑓(𝑥^∗𝑗)
0	(0.4528408,0.8017877,2.580122,−1.214387)	0.1	1.0	3.203103	4.425251	1.858834	−53.31968
1	(0.2167079,0.8595678,2.192063,−1.159403)	0.1×5	10^−1	0.7715020	1.643783	−0.039055	−47.79021
2	(0.1782670,0.8383819,2.051085,−1.015255)	0.1×5^2	10^−2	0.1530515	0.3785772	−1.457033	−45.08350
3	(0.1712600,0.8356738,2.017540,−0.9755791)	0.1×5^3	10^−3	0.030094	0.078609	−1.795672	−44.41169
4	(0.1696707,0.8354126,2.010606,−0.9668932)	0.1×5^4	10^−4	0.005887	0.015878	−1.865860	−44.26973
5	(0.1836584,0.8497245,1.993892,−0.9809219)	0.1×5^5	10^−5	0.001217	0.002323	−1.824922	−44.23592
6	(0.1835818,0.8496645,1.993588,−0.9808556)	0.1×5^6	10^−6	−0.000298	0.000466	−1.826614	−44.23108
7	(0.1843284,0.8502323,1.992886,−0.9814753)	0.1×5^7	10^−7	−0.000141	0.000219	−1.824903	−44.23038
8	(0.1843219,0.8502275,1.992824,−0.9814662)	0.1×5^8	10^−8	−0.000412	−0.000131	−1.825209	−44.22948