Can we dynamically extract some information and strong relationship between some financial features in order to select some financial trades over time? Despite the advent of representation learning and end-to-end approaches, mainly through deep learning, feature selection remains a key point in many machine learning scenarios. This paper introduces a new theoretically motivated method for feature selection. The approach that fits within the family of embedded methods, casts the feature selection conundrum as a coordinate ascent optimization with variables dependencies materialized by block variables. Thanks to a limited number of iterations, it proves efficiency for gradient boosting methods, implemented with XGBoost. In case of convex and smooth functions, we are able to prove that the convergence rate is polynomial in terms of the dimension of the full features set. We provide comparisons with state of the art methods, Recursive Feature Elimination and Binary Coordinate Ascent and show that this method is competitive when selecting some financial trades.