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Learn about implementing Algorithm NCL on GPUs for smooth constrained optimization problems in this 25-minute invited talk. Discover how Algorithm NCL serves as an equivalent to the augmented Lagrangian algorithm of LANCELOT while being immune to LICQ (Linear Independence Constraint Qualification) difficulties and requiring only about 10 subproblems to be solved using interior methods and second derivatives. Explore the transition from AMPL implementation using IPOPT or KNITRO to GPU utilization through MadNLP.jl, a nonlinear interior method designed for GPU computing, and CUDSS.jl, which provides a Julia interface to the NVIDIA cuDSS library. Understand how the NCL transformation enables KKT systems to be reduced to smaller, more manageable systems that can be efficiently solved using Cholesky-type factorization, and examine numerical experiments demonstrating the effectiveness of this GPU-based approach to constrained optimization.
