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Table 2 Numerical results for Example 4.1 with \(\pmb{k=2/3}\)

From: Smoothing of the lower-order exact penalty function for inequality constrained optimization

j

\(\boldsymbol {x_{j}^{*}}\)

\(\boldsymbol {q_{j}}\)

\(\boldsymbol {\epsilon_{j}}\)

\(\boldsymbol {g_{1}(x_{j}^{*})}\)

\(\boldsymbol {g_{2}(x_{j}^{*})}\)

\(\boldsymbol {f(x_{j}^{*})}\)

0

\(\Bigl( \begin{array}{@{}c@{}} 0.725362\\ 0.399226 \end{array} \Bigr)\)

10

0.1

0.775917

0.000175

1.715609

1

\(\Bigl( \begin{array}{@{}c@{}} 0.725353 \\ 0.399257 \end{array} \Bigr)\)

20

0.01

−0.775869

0.000000

1.837547