An augmented Lagrangian interior-point approach for large-scale NLP problems on graphics processing units

• A parallel NLP algorithm is developed for graphics processing units (GPU).
• GPU is used for parallel PCG (solving KKT system) and function evaluations.
• Parallel implementation shows an order of magnitude speedup on test problems.

The demand for fast solution of nonlinear optimization problems, coupled with the emergence of new concurrent computing architectures, drives the need for parallel algorithms to solve challenging nonlinear programming (NLP) problems. In this paper, we propose an augmented Lagrangian interior-point approach for general NLP problems that solves in parallel on a Graphics processing unit (GPU). The algorithm is iterative at three levels. The first level replaces the original problem by a sequence of bound-constrained optimization problems using an augmented Lagrangian method. Each of these bound-constrained problems is solved using a nonlinear interior-point method. Inside the interior-point method, the barrier sub-problems are solved using a variation of Newton's method, where the linear system is solved using a preconditioned conjugate gradient (PCG) method, which is implemented efficiently on a GPU in parallel. This algorithm shows an order of magnitude speedup on several test problems from the COPS test set.