I wanted to clarify the idea of the exact line search in steepest descent method. An exact line search involves starting with a relatively large step size ($\alpha$) for movement along the search direction $(d)$ and iteratively shrinking the step size until a decrease of the objective function is observed. Is this correct?I.e. the only condition suppose to be satisfied is: $f(x_{k+1})<f(x_k)$, where $x_{k+1} = x_k + \alpha_kd_k$In exact line search the step size $\alpha$ is not necessary to be fixed. Is this true?If this is true then what is the difference of the exact line search from the backtracking line search? I know that backtracking line search is based on Armijo-Gooldstein condition or Wolfe's condition. 
Exact line Search in Steepest descent
optimization;algorithms;numerical analysis