svm-linesearch.m

  % Backtracking line search until constraints are met. We decompose deltaY 
    deltaX = deltaY(1:n); 
    deltaL = deltaY(n+1:n+m);
    deltaN = deltaY(n+m+1:end); %delta nu
    
    s_max = 1;
    s = s_max;
    
    nIterBT = 0;
    stopCondBackTrack = false;
    
        while(~stopCondBackTrack && nIterBT < opts.maxIter)
        %check if constrints are satisfied
        if ((max(ineqConstraint.f(x_k + s*deltaX)) < 0) && (norm(res(t, x_k + s*deltaX, lambda_k + s*deltaL, nu_k + s*deltaN)) <= (1 - opts.alpha*s)*norm(res_k)))
            stopCondBackTrack = true;
        else       
          s = opts.beta*s;
          nIterBT = nIterBT + 1;
        end
    end
    
    % Updating our points
    x_k = x_k + s*deltaX;
    lambda_k = lambda_k + s*deltaL;
    nu_k = nu_k + s*deltaN;