How to determine Simplex using Nelder-Mead Algorithm in all direction?

Dear All, how can I determine all the possibles simplexes while working with Nelder-Mead Algorithm? Please have a look into the illustrated picture along with codes.

function [xMin] = NMS2(objfunc,x0,alpha,beta,gamma,varargin)
    N = length(x0);
    
    % Initializing the simplex
    smp = repmat(x0,1,N+1);
    smp(:,2:end) = smp(:,2:end) + eye(N);
        
    % Identify the vertices 
    fval = feval(objfunc,smp,varargin{:});
    
    iter = 0;TOL = 1e-8; maxIter = 500*N;
   
    while iter <= maxIter
    
        % sort function values in ascending order
        [fval,I2] = sort(fval);
        smp = smp(:,I2);
        
        v0 = smp(:,1);
        f0 = fval(1);
        
        fStd = std(fval);
        distv0 = max(max(abs(repmat(v0,1,N)-smp(:,2:end))));
        if fStd < TOL && distv0 < TOL
            break;
        end
        
        vn = smp(:,N+1);
        fn = fval(N+1);

        %calculate the centroid over all vertices vi ~= vn
        vert = mean(smp(:,1:N),2);

This is the partial code along with stopping condition.

[James Tursa]

I don't understand the question. What do you mean by "determine all the possible simplexes"?

[Julkar_Mustakim]

Dear James Tursa, If you have a look into the picture you will understand what I meant. Usually we find the simplex based on three points (V0,V1 & V2). But in this case the intial simplex could be any three points in any direction where "V0" is fixed but "V1 and V2" could be anywhere around "V0" like the way it is mentioned in the picture. I hope, I clarified the method. Thank you.

Answer 1

[James Tursa]

The Nelder-Mead Simplex Method is an adaptive method that adjusts the lengths and directions dynamically. The vertices could be anywhere on your plot above (and outside of it), not just at the square corner points and mid-points. So your desire to determine all possible simplexes simply doesn't make sense for this algorithm. There are an infinite number of them and an infinite variety of shapes and sizes.

[Julkar_Mustakim]

Dear James, thanks for your answer. So it is possible to assign the points statically instead of dynamically around the point "V0"? Thank you.