Hello myforework,
no, that method is not implemented in ATENA. However, according to our experience, in most cases, convergence issues are a consequence of some problem(s) in the modelling (from such trivial as missing supports to more complicated ones which are not so obvious), see also ATENA Troubleshooting, 2.4.2 I get the message "The execution is killed due to violation of stop iteration criteria", what does it mean?, 2.4.6 Floating point problems - Division by zero, Loss of >7 digits on the matrix diagonal, CCFEModelExc: CCPardiso solver error: zero pivot,  Warning: Sign of diagonal changed when reducing equation, Floating point exception: Multiple floating points traps, Zero or negative jacobian,  InvertA: zero determinant, CCMaterials Extended AExc: CC5ParamYield F: project_stress_on_f_division by zero, and similar, 2.1.19 Problems reaching convergence and understanding ATENA convergence parameters, and 2.2.22 How to detect a structural collapse or ultimate load capacity.

However, I am noting BFGS (or more likely some of its limited memory variants) to the list of ideas for possible future development.

Regards.