<p>In this paper, we are interested in solving optimization programs whose objective function is expressed as the ratio of two real-valued functions, with block-separable constraints. This kind of problems is difficult due to a possible lack of convexity and is more difficult in the case of large sizes. For this, we propose two algorithms that are based on the block coordinate method: Dinkelbach and the proximal point algorithms. In these algorithms, the decision variable is partitioned into blocks of coordinates, and at each iteration, the intermediate problems are solved successively with respect to each block, while keeping the other blocks fixed. We establish that every cluster point of the sequences generated by the two algorithms satisfies optimality conditions expressed in terms of directional derivatives. Finally, we solve numerical problems to illustrate the behavior of our algorithms.</p>