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Table 1 Numerical results for Example 4.1 with \(x^{0}=(0,0,0,0)\)

From: Smoothing approximation to the lower order exact penalty function for inequality constrained optimization

j

\(x^{j+1}\)

\(q_{j}\)

\(\epsilon_{j}\)

\(f_{1}(x^{j+1})\)

\(f_{2}(x^{j+1})\)

\(f_{3}(x^{j+1})\)

\(f_{0}(x^{j+1})\)

0

(0.185009,0.804369,2.015460,−0.952409)

1

0.01

−4.797079

−0.00109

−2.028111

−44.225926

1

(0.169902,0.835670,2.008151,−0.965196)

2

0.0001

−9.748052

−9.337847

−1.883271

−44.231252