A United Probabilistic Approach to Minimising the Sum of Absolute Values

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.