liste vertex into polyhedron

Can I list all vertexes of polyhedron into this format ?

Ax<=b

x>=0

A is matrix

Answer 1

[Matt J]

See lcon2vert in this FEX download, which does not require the Optimization Toolbox,

https://www.mathworks.com/matlabcentral/fileexchange/90762-further-tools-for-analyzing-objects-in-n-dimensional-images

Answer 2

[Naga]

Hello Riccardo,

I understand that you are trying to list all the vertices of a polyhedron in MATLAB by solving the system of inequalities Ax<=b and x>=0. MATLAB does not have a built-in function specifically for listing all vertices of a polyhedron, but you can use the `linprog` function to find vertices.

1. Define the Polyhedron: Start with the matrix \(A\) and vector \(b\) that define your polyhedron.

2. Use `linprog` to Find Vertices: You can use linear programming to find the vertices by solving optimization problems for each combination of constraints.

Here is a MATLAB script to list all the vertices of a polyhedron:

function vertices = findPolyhedronVertices(A, b)
    % Number of variables
    n = size(A, 2);

    % All combinations of constraints
    combs = nchoosek(1:size(A, 1), n);

    % Initialize an empty array to store the vertices
    vertices = [];

    % Solve for each combination of constraints
    for i = 1:size(combs, 1)
        % Select the constraints
        A_eq = A(combs(i, :), :);
        b_eq = b(combs(i, :));

        % Solve the linear system A_eq * x = b_eq
        x = A_eq \ b_eq;

        % Check if the solution is feasible
        if all(A * x <= b) && all(x >= 0)
            % Add the vertex to the list
            vertices = [vertices, x];
        end
    end

    % Remove duplicate vertices
    vertices = unique(vertices', 'rows')';
end
 
% Example usage:
A = [1 1; 1 -1; -1 0; 0 -1];
b = [2; 1; 0; 0];
 
vertices = findPolyhedronVertices(A, b);
 
% Display vertices in a readable format
disp('Vertices of the polyhedron:');
for i = 1:size(vertices, 2)
    fprintf('Vertex %d: (%.4f, %.4f)\n', i, vertices(1, i), vertices(2, i));
end