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Table 1 Numerical results for Example 4.1 with \(\pmb{k=1/3}\)

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

\(\Bigl( \begin{array}{@{}c@{}} -0.362270\\ 0.366667 \end{array} \Bigr)\)

1

0.1

3.154764

−0.224317

1.277367

1

\(\Bigl( \begin{array}{@{}c@{}} 0.724975 \\ 0.399152 \end{array} \Bigr)\)

2

0.01

−0.774989

−0.000000

1.837569