Theoretical justification of a heuristic subbox selection criterion for interval global optimization (Q5957418)

A global optimization technique based on interval arithmetic is considered. A criterion is proposed to select a box for sub-division in a branch and bound procedure: \( \frac{\tilde{f}-\underline{F}(X)}{\overline{F}(X)-\underline{F}(X)}\) where \(X\) denotes a box. It is proven that the proposed criterion is invariant with respect to some natural symmetries and is optimal in some reasonable sense.