<p>In this paper, we propose a second-order descent algorithm with an active-set prediction phase for solving group-sparse nonconvex optimization problems, with applications to PDE-constrained optimization. Based on the steepest descent direction of the nonsmooth problem, we propose an active-set prediction strategy, which relies on an iterative interpretation of the problem’s optimality condition, determining the active set for the next iteration based on the angle between the current iterate and the descent direction for each group. The constructed descent direction is then combined with generalized Hessian information to form a second-order descent direction. We demonstrate that our method rapidly identifies the active and inactive groups at the optimal solution and converges both globally, and locally at a <i>q</i>-quadratic rate. Finally, we conduct comparative computational experiments to evaluate the algorithm’s performance.</p>