Weakest Link, Harmonic Increment, and Crossed Ladders
Published: 29.10.26 — A harmonic increment provides a new way to improve smooth approximations of the minimum function. In a recent paper, published in the Journal of Inequalities and Applications, Prof. Thomas A. Weber shows how a harmonic-increment transformation brings any smooth estimate that lies strictly below the minimum closer to it, while keeping the improved estimate below the minimum, so it remains a conservative estimate of a worst realization, or weakest link. The method also provides explicit error guarantees. Its inner workings can be illustrated by a recursive construction based on the classical crossed-ladders problem. More broadly, it offers a tool for models of production bottlenecks and other systems governed by their smallest input.