OptimizationTechniques/Work 3/scripts/gamma_minimized.m

function [gamma] = gamma_minimized(f, ~, dk, xk)
    % Calculates the step based on minimizing f(xk​− γk*dk)
    %
    %
    % f:    Objective function
    % ~:    Gradient function of f - Not used
    % dk:       Current value of selected direction -∇f or -inv{H}*∇f or -inv{H + lI}*∇f
    % xk:   Current point (x,y)

    % Define the line search function fmin(g) = f(xk - g * dk)
    fmin = @(g) f(xk) + g * dk;

    % find g that minimizes fmin
    e = 0.0001;
    l = 0.001;
    [a,b,k,~] = fmin_bisection(fmin, 0.0001, 1, e, l);   % g in (0, 1]
    gamma = 0.5*(a(k) + b(k));

    % Define the line search function fmin(g) = f(xk - g * dk)
    %fmin = @(g) f(xk(1) - gamma * dk(1), xk(2) - gamma * dk(2));

    % find g that minimizes fmin
    %gamma = fminbnd(g, 0, 1);
end