Uniform approximation of min/max functions by smooth splines

In some optimization problems, min(f1,…,fn)min(f1,…,fn) usually appears as the objective or in the constraint. These optimization problems are typically non-smooth, and so are beyond the domain of smooth optimization algorithms. In this paper, we construct smooth splines to approximate min(f1,…,fn)min(f1,…,fn) uniformly so that such optimization problems can be dealt with as smooth ones.