Chebyshev Problem

Find the center and radius of the shortest or smallest circumference of a set of points with MATLAB.

Problem to solve 📑

This is a Nonlinear Optimization problem that consists in: we are given a set of points a₁,a₂,...,a_m ∈ ℝⁿ, and we seek to find a point x ∈ ℝⁿ , which is the center of the minimum radius ball containing the points

For more information read Smallest-circle problem and Optimal-Separation of Points

Input 📋

The main program is called ChebyshevProblem.m, which is the program to compile. You have to change matrix A to modify the set of points.

The first row corresponds to the x coordinate, while the second row corresponds to the y coordinate, that is, each column is a point.

Output 📦

• Center of the ball
• Minimun radius
• Graphic

The code base was obtained from the book Introduction to Nonlinear Optimization Theory, Algorithms and Applications.