A United Probabilistic Approach to Minimising the Sum of Absolute Values - Feng, Changyong; Liu, Honghong; Poon, Ethan; Feng, Ge (Zunifikowane probabilistyczne podejście do minimalizacji sumy wartości bezwzględnych, 2024)
Aim: Introduce a novel method for minimizing functions in the form of a sum of absolute values. Methodology: The sum of absolute values can be standardized so that the sum of the coefficients equals 1. In this case, the sum of absolute values takes the form 𝐸𝐸|𝑋𝑋−𝑎𝑎|, where 𝑋𝑋 is a random variable. Results: Any median of 𝑋𝑋 is a minimiser of the function 𝐸𝐸|𝑋𝑋−𝑎𝑎|. To minimise the function, it suffices to find any median of 𝑋𝑋. Implications and recommendations: The method introduced in this paper can be applied to minimise a large family of functions. Originality/value: Our work uses the probabilistic method to solve optimization problems.
Econometrics = Ekonometria, 2024, Vol. 28, No. 3, s. 1-8
Keywords: median; probability distribution; minimum value; mediana; rozkład prawdopodobieństwa; wartość minimalna