[en] This paper is dedicated to a new convex separable approximation for solving optimization problems characterized by a very large number of design variables as in topology design. For such problems, the convergence speed can be accelerated if one uses high quality approximation schemes for structural responses. To achieve this task, we propose, here, a new approximation procedure that belongs to the GMMA family. The originality of this new scheme is to rely on an automatic selection procedure of the asymptotes, using only first and zero order information accumulated during the previous iterations. This is possible owing to a diagonal Quasi-Newton update technique. Firstly, the new approximation procedure is validated on classical "benchmarks" of structural optimization. Then, it is compared to other schemes on a typical topology optimization problem.