Peer-reviewedCC BYJournal of Inequalities and Applications
Smooth approximation of the minimum function from below (and above)
- 1Chair of Operations, Economics and Strategy, École Polytechnique Fédérale de Lausanne
Abstract
We provide an increasing approximating sequence of smooth lower bounds for the minimum of n ≥ 2 n≥ 2 real numbers, with exponential convergence. For any given strict lower bound, we obtain a strict improvement through a harmonic increment. Additionally, we compute the maximum relative and absolute errors and construct a smooth approximating sequence from above using the geometric mean. Closed-form expressions are provided for the case n = 2 n = 2 , where the solution relates to the well-known crossed-ladders problem.
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BibTeX
@article{weber2026smooth,
title = {{Smooth approximation of the minimum function from below (and above)}},
author = {Thomas A. Weber},
journal = {Journal of Inequalities and Applications},
year = {2026},
month = jul,
doi = {10.1186/s13660-026-03519-3},
url = {https://doi.org/10.1186/s13660-026-03519-3},
note = {CC BY},
}
RIS
TY - JOUR
TI - Smooth approximation of the minimum function from below (and above)
AU - Thomas A. Weber
PY - 2026
DA - 2026/07/01
JO - Journal of Inequalities and Applications
DO - 10.1186/s13660-026-03519-3
UR - https://doi.org/10.1186/s13660-026-03519-3
AB - We provide an increasing approximating sequence of smooth lower bounds for the minimum of n ≥ 2 n≥ 2 real numbers, with exponential convergence. For any given strict lower bound, we obtain a strict improvement through a harmonic increment. Additionally, we compute the maximum relative and absolute errors and construct a smooth approximating sequence from above using the geometric mean. Closed-form expressions are provided for the case n = 2 n = 2 , where the solution relates to the well-known crossed-ladders problem.
SN - 1029-242X
ER -