Backtracking Armijo-Type

It's used into a linesearch method, to compute how far one should move along a given direction

In (unconstrained) optimization, the backtracking linesearch strategy is used as part of a line search method, to compute how far one should move along a given search direction. It's an advanced strategy with respect to classic Armijo method.
It's a search method along a coordinate axis in which the search should be conducted in both directions of the axis. It should also take into account the fact that one direction dk can be assigned such that alpha=0 represents a local minimum point of the function g(alpha)=F(xk+alpha*dk), for which may not be able to find positive or negative values for alpha close to 0 for which g(alpha)<g(0). If you do not want to use any derivative, numerical "finished" procedures must define can discriminate the situation. The model presented is an outline Backtracking Armijo-type, based on the condition of acceptability of type "Parabolic".