In many matrix completion problems, the rank of the unknown target matrix is known in advance and this information can be useful in the completion process. In this talk, first, we shall revisit a recently proposed rank-based heuristic for “known-rank” matrix completion and establish a condition under which the generated sequence is quasi-Fejér convergent to the solution set. Even though such condition cannot be granted in general, it turns out that the heuristic can be very useful as a warm-start phase, providing a suitable estimate for the regularization parameter as well as a good starting point to an accelerated proximal gradient algorithm to solve a nuclear-norm regularized problem. Numerical experiments with both synthetic and real data illustrate the performance of the resulting algorithm in completion problems where the target rank is known as is the case of Euclidean Distance Matrix Completion Problems. This is a joint work with Tacildo Araújo and Cristiano Torezzan.