MultidimNewtonsODSA.m

%% Newton's ODSA to be used in another opt. method as ODSA %%
% func: Symbolic function
% a: Lowerbound
% b: Upperbound
% e: Precision
% p: Dummy parameter for convention
% max_iter: Number of iterations
% t: Equation of symbolic input
% u: Symbolic input

function t = MultidimNewtonsODSA(func, a, b, e, p, max_iter, t, u)
    init = (a+b)/2;
    m = mat2cell(t,1,ones(1,numel(t)));
    r = func(m{:});
    z = matlabFunction(r,'vars', u); 
    x1 = init;
    x2 = init;
    df1 = Differentiate(z, u);
    df2 = Differentiate(df1, u);
    to = CalculateFunctions(df1, u, x1);
    while to > e && i < max_iter
        x2 = x1 - to/(CalculateFunctions(df2, u, x1));
        to = CalculateFunctions(df1, u, x2);
        x1 = x2;
    end
    t = x2;
end

%{
Example usage

syms x y e
f = @(x, y) 0.7*x^4 - 8*x^2 + 6*y^2 + cos(x*y) - 8*x;

u = [e];
o = [1 2] + e*[4 5];

res = MultidimGoldenSectionSearch(f, -0.5, 0.5, 10^-5, 50, o, u);
disp(res);
%}