OptimizationTechniques/Work2/scripts/gamma_armijo.m

function [gamma] = gamma_armijo(f, grad_f, dk, xk)
    % Calculates the best step based on amijo method
    %
    % f(xk​+ γk*dk) ≤ f(xk) + σ * γk * dk^T * ∇f(xk)
    % γk = β*γk_0
    %
    % f:        Objective function
    % grad_fun: Gradient function of f
    % dk:       Current value of selected direction -∇f or -inv{H}*∇f or -inv{H + lI}*∇f
    % xk:       Current point (x,y)
    
    
    % beta:     beta  factor in [0.1, 0.5]
    % signam:   sigma factor in (0, 0.1]
    global amijo_beta
    global amijo_sigma

    gf = grad_f(xk(1), xk(2));
    gamma = 1; % Start with a step size of 1

    % Perform Armijo line search
    while f(xk(1) + gamma * dk(1), xk(2) + gamma * dk(2)) > ...
          f(xk(1), xk(2)) + amijo_sigma * gamma * dk' * gf
    %while f(xk(1) + gamma * dk(1), xk(2) + gamma * dk(2)) > ...
    %      f(xk(1), xk(2)) + amijo_sigma * gamma * norm(dk)^2
        gamma = amijo_beta * gamma; % Reduce step size
        if gamma < 1e-12 % Safeguard to prevent infinite reduction
            warning('Armijo step size became too small.');
            break;
        end
    end

end