Work

Smooth approximation of the minimum function from below (and above)

Year: 2026

Type: article

Abstract: We provide an increasing approximating sequence of smooth lower bounds for the minimum of $n\geq 2$ 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.

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-026-03519-3

Author: Thomas A. Weber

Institution: École Polytechnique Fédérale de Lausanne

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,190

Funder: École Polytechnique Fédérale de Lausanne