A separable augmented Lagrangian algorithm for optimal structural design

We propose an iterative separable augmented Lagrangian algorithm (SALA) for optimal structural design, with SALA being a subset of the alternating directions of multiplier method (ADMM)–type algorithms. Our algorithm solves a sequence of separable quadratic-like programs, able to capture reciprocal- and exponential-like behavior, which is desirable in structural optimization. A salient feature of the algorithm is that the primal and dual variable updates are all updated using closed-form expressions. Since algorithms in the ADMM class are known to be very sensitive to scaling, we propose a scaling method inspired by the well-known ALGENCAN algorithm. Comparative results for SALA, ALGENCAN, and the Galahad LSQP solver are presented for selected test problems. Finally, although we do not exploit this feature herein, the primal and dual updates are both embarrassingly parallel, which makes the algorithm suitable for implementation on massively parallel computational devices, including general purpose graphical processor units (GPGPUs).