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We present the implementation of a trust-region Newton algorithm ExaTron forbound-constrained nonlinear programming problems, fully running on multipleGPUs. Without data transfers between CPU and GPU, our implementation hasachieved the elimination of a major performance bottleneck under a memory-boundsituation, particularly when solving many small problems in batch. We discussthe design principles and implementation details for our kernel function andcore operations. Different design choices are justified by numericalexperiments. By using the application of distributed control of alternatingcurrent optimal power flow, where a large problem is decomposed into manysmaller nonlinear programs using a Lagrangian approach, we demonstratecomputational performance of ExaTron on the Summit supercomputer at OakRidgeNational Laboratory. Our numerical results show the linear scaling withrespect to the batch size and the number of GPUs and more than 35 times speedupon 6 GPUs than on 40 CPUs available on a single node.

Leveraging GPU batching for scalable nonlinear programming through massive Lagrangian decomposition