ExaModels.jl: an Algebraic Modeling System for Nonlinear Programming on GPUs

Abstract

Large-scale nonlinear programs almost always exhibit partially separable and repetitive structure, yet most existing algebraic modeling systems do not take advantage of it. A nonlinear optimization solver queries the objective, the constraints, and their derivatives at every iteration, so the speed of these evaluations bears directly on the overall solution time. We present ExaModels.jl, a Julia-based algebraic modeling system that exploits this structure to evaluate the objective, the constraints, and their derivatives in parallel. At its core is a single-instruction, multiple-data abstraction that represents a nonlinear program as a small number of algebraic patterns, each repeated over many data points. Because the patterns are visible at compile time, a specialized model and derivative evaluation kernel is compiled for each pattern. Applying that kernel independently across the data points maps naturally onto GPU parallelism and, with sufficiently many threads, yields O(1) evaluation time regardless of the number of data points. On the largest instances of the Luksan-Vlcek library, GPU execution speeds up sparse Hessian evaluation by 76x over single-threaded CPU evaluation, and by 30x on COPS and 7.3x on PGLIB-OPF.