Publication Date



Technical Report: UTEP-CS-13-44

To appear in Journal of Uncertain Systems, 2014, Vol. 8.


In many practical situations, we need to minimize an expression of the type |c1| + ... + |cn|. The problem is that most efficient optimization techniques use the derivative of the objective function, but the function |x| is not differentiable at 0. To make optimization efficient, it is therefore reasonable to approximate |x| by a smooth function. We show that in some reasonable sense, the most computationally efficient smooth approximation to |x| is the function √(x2 + μ), a function which has indeed been successfully used in such optimization.