The log-exponential smoothing technique and Nesterov's accelerated gradient method for generalized Sylvester problems (Q274096)

The authors consider a generalization of the Sylvester problem. It consists in finding the smallest ball that intersects a finite number of target sets in \(\mathbb R^n\). When the sets are singeltons, the problem reduces to the classical Sylvester problem. The authors propose a numerical algorithm for solving the generalized Sylvester problem based on the log-exponential smoothing technique and Nesterov's accelerated gradient method. Numerical examples in the concluding section of the paper show that the proposed algorithm is effective also for problems in higher dimensions.