Solving the smallest ball problem based on convex programming theories

Abstract

The mathematical method known to be Quadratic Programming is a branch of Convex Programming or Convex Optimization, which is then a peculiar case of Mathematical Optimization given a series of restrictions including a convex function to minimize. The Smallest Ball Problem is a problem where we seek to find the smallest enclosing ball of given points on a plane. Convex Optimization provides a solution to the Smallest Ball Problem. There are several ways to characterize a convex programming problem and its solutions, the most important of which is called the KKT conditions. By relating the Smallest Ball Problem to solving a Convex Programming Problem and using the Python packages, the radius, as well as the central point of the Smallest Ball, will be found. In addition, the underlying algorithm for solving Convex Programming Problems is studied. It can be concluded that Convex Programming, or more specifically, Quadratic Programming, gives a feasible solution to the Smallest Ball Problem.