The Log-Exponential Smoothing Technique and Nesterov's Accelerated Gradient Method for Generalized Sylvester Problems

TL;DR

This paper introduces a novel numerical algorithm combining log-exponential smoothing and Nesterov's accelerated gradient method to efficiently solve generalized Sylvester problems involving set enclosures.

Contribution

The paper develops a new algorithm that extends classical Sylvester problems to sets using advanced optimization techniques.

Findings

Effective numerical solutions for generalized Sylvester problems.

Algorithm demonstrates improved convergence properties.

Applicable to various set enclosure problems.

Abstract

The Sylvester smallest enclosing circle problem involves finding the smallest circle that encloses a finite number of points in the plane. We consider generalized versions of the Sylvester problem in which the points are replaced by sets. Based on the log-exponential smoothing technique and Nesterov's accelerated gradient method, we present an effective numerical algorithm for solving these problems.