function seq = BR_Newton_MP(tol,a0,b0,max_iter,alpha,r,n)
% move to lowest surounding point
% seq0 = BR_Newton_MP(0.000001,0.5,0.5,4000,0.001,0.01,21);

a = a0;
b = b0;
f = BR_f_MP(a,b); 
seq = [a0,b0,f,0,0];
H = zeros(2,2);
DEL = zeros(2,1);
iter = 0;
ring = zeros(1,n);
while tol<f&(iter<max_iter)
    iter = iter + 1;
    H(1,1) = 4 - 4*b + 2*b^2;
    H(1,2) = 0.6 - 4*a +4*a*b;
    H(2,1) = H(2,1);
    H(2,2) = 2*a^2;
    DEL(1) = 4*a + 0.6*b - 4*a*b + 2*a*b^2 - 2;
    DEL(2) = 0.6*a - 2*a^2 + 2*(a^2)*b;
    del_theta = atan2(DEL(2),DEL(1));
    s = alpha*(H\DEL);
    fs = BR_f_MP(a,b);
    theta = [pi/(n-1):pi/(n-1):2*pi];
    ar = a + r*cos(theta);
    br = b + r*sin(theta);
    fr = BR_f_MP(ar,br);
    [vv,ii] = min(fr);
    t = theta(ii);
    a = a + alpha*cos(t);
    b = b + alpha*sin(t);
    f = fs;
    del = DEL/norm(DEL);
    seq = [seq; a,b,f,del_theta,t];
end
