A maximum entropy method for constrained semi-infinite programming problems (Q2721873)

The semi-infinite problem \(\min \{ f( x) \mid \Phi ( x,\omega) \leq 0\) \(\forall _{\omega \in \Omega }\}\) for a compact body \(\Omega \) of \(\mathbb{R}^{n}\) is considered by using in Sections 1 and 2 a \(p\) parametric entropy regularization identically to \textit{Shu-Cherng Fang, J. R. Rajasekera} and \textit{H.-S. J. Tsao} [Entropy optimization and mathematical programming (1997; Zbl 0933.90051) pp. 311-319]. The regularization is solved in Section 3 by Rockafellar's augmented Lagrange method for fixed large enough \(p\) . Five numerical examples are given. However, the effort and the troubles for computing the integral regularization, which contains an exponential function with absolutely large exponents in the integrand, are not discussed.