  In this work, we explore the use of operator splitting algorithms for solving
regularized structural topology optimization problems. The context is the
classical structural design problems (e.g., compliance minimization and
compliant mechanism design), parameterized by means of density functions, whose
ill-posendess is addressed by introducing a Tikhonov regularization term. The
proposed forward-backward splitting algorithm treats the constituent terms of
the cost functional separately which allows suitable approximations of the
structural objective. We will show that one such approximation, inspired by the
optimality criteria algorithm and reciprocal expansions, improves the
convergence characteristics and leads to an update scheme that resembles the
well-known heuristic sensitivity filtering method. We also discuss a two-metric
variant of the splitting algorithm that removes the computational overhead
associated with bound constraints on the density field without compromising
convergence and quality of optimal solutions. We present several numerical
results and investigate the influence of various algorithmic parameters.
