Modeling and Optimization of Control Problems on GPUs

We present a fully Julia-based, GPU-accelerated workflow for solving large-scale sparse nonlinear optimal control problems. Continuous-time dynamics are modeled and then discretized via direct transcription with $\mathtt{\text{OptimalControl.jl}}$ into structured sparse nonlinear programs. These programs are compiled into GPU kernels using $\mathtt{\text{ExaModels.jl}}$, leveraging SIMD parallelism for fast evaluation of objectives, constraints, gradients, Jacobians and Hessians. The resulting sparse problems are solved entirely on GPU using the interior-point solver $\mathtt{\text{MadNLP.jl}}$ and the GPU sparse linear solver cuDSS, yielding significant speed-ups over CPU-based approaches.