I am trying to compare many unconstrained optimization algorithms like gradient method, Newton method with line search, Polak-Ribiere algorithm, Broyden-Fletcher-Goldfarb-Shanno algorithm, so on so forth. For these methods, I use Armijo line search method to determine how much to go towards a descent direction at each step.

As commonly known, the Armijo condition requires some parameter selection (namely the distance to go $\alpha$, the coefficient that will multiply $\alpha$ at each step which is $\sigma$, and some $\gamma \in (0, 1/2)).$ I am not familiar with a way of choosing the best set of parameters. I could imagine they would differ from problem to problem, but what is the most common way to decide these parameters?


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