# A dual Simplex-type algorithm for the smallest enclosing ball of balls and related problems

## TL;DR

This paper introduces a dual Simplex-type algorithm for finding the smallest enclosing ball of balls, extending the classical simplex method to second order cone problems and related geometric optimization tasks.

## Contribution

It proposes a novel dual algorithm that generalizes the simplex method for second order cone problems, addressing the smallest enclosing ball of balls and related issues.

## Key findings

- Algorithm effectively solves the smallest enclosing ball of balls problem
- Extends simplex method to second order cone optimization
- Applicable to related geometric problems

## Abstract

We define the notion of infimum of a set of points with respect to the second order cone. This problem can be showed to be equivalent to the minimum ball containing a set of balls problem and to the maximum intersecting ball problem, as well as others. We present a dual algorithm which can be viewed as an extension of the simplex method to solve this problem.