Hi. I don't know it steepest descend is part of any of the Matlab toolbox (anyway, you can find a version here: https://fr.mathworks.com/matlabcentral/fileexchange/22532-steepest-descent-algorithm), but you can use the standard method fminsearch, which in this case works quite well, because the problem is very simple:
% Setup the problem
X0 = [0 10];
fun = @(X) 5*X(:,1).^2 + X(:,2).^2 + 4*X(:,1).*X(:,2) - 14*X(:,1) - 6*X(:,2) + 20;
% Perform the optimization (indeed not by using the steepest descent algorithm)
options = optimset('Display','iter', 'TolX', 1E-6);
[X,FVAL,EXITFLAG] = fminsearch(fun, X0)
Let's check if the result is reasonable:
[x, y] = meshgrid(-2:0.1:3, -2:0.1:3);
f = reshape(fun([x(:) y(:)]), size(x));
figure
mesh(x, y, f) ; hold on ; plot3(X(1), X(2), FVAL, 'r*') ; view(30, 60);
To be 100% sure, let's do some analytical computing:
syms x1 x2
f = 5*x1^2 + x2^2 + 4*x1*x2 - 14*x1 - 6*x2 + 20;
jac = jacobian(f)
det([10 4 ; 4 2])
The jacobian matrix is constant, and it is not singular: hence it exists only one solution:
solve(jac)
