Exact penalty functions for nonlinear integer programming problems
The authors first find a set of sufficient conditions under which the nonlinear problem \(\min \{ f(x) \, : \, x\in W \}\) has the same minimum point(s) as each member of the family \(\min \{ f(x)+\phi (x, \varepsilon) \, : \, x\in X \}\) (\(0<\varepsilon < \overline{\varepsilon} \)). Here \(W\subseteq X \subseteq \mathbb R ^n\), \(f,\phi (\cdot , \varepsilon) : \mathbb R ^n\longrightarrow \mathbb R\) and \(\overline{\varepsilon} \) is a positive number, depending on \(W\), \(X\), \(f\), and \(\phi\). Then they provide 6 explicit penalty terms \(\phi (\cdot, \varepsilon)\) in case \(W\subseteq \{ 0,1 \}^n\), and 2 additional ones valid for a general integer programming problem.
scientific article; zbMATH DE number 5760462