An interval entropy penalty method for nonlinear global optimization (Q1383743)

Constrained max-max problems such as \(\max\| f\|_\infty\) subject to a feasible domain, \(X\), are considered. Two approaches are discussed. The first one uses ideas of \textit{A. B. Templeman} and \textit{X. Li} [Eng. Opt. 12, 191-205 (1987)] who replace the objective function, \(\| f\|_\infty\), where \(f\) is smooth, by a smooth approximation. Similarly, the constraint functions are combined to a smooth penalty term, which is called entropy penalty function. The error which arises by this smoothing procedure can be estimated. This concept is generalized to max-max problems where Lipschitz continuous functions are involved. The second approach uses standard interval branch-and-bound methods to solve optimization problems over a box, where the objective function is Lipschitz continuous.