NLPOpt-Net: A Learning Method for Nonlinear Optimization with Feasibility Guarantees

We introduce the Nonlinear Parametric Optimization Network (NLPOpt-Net), an unsupervised learning architecture for solving parametric nonlinear programs (NLPs) across varying parameter instances while guaranteeing constraint feasibility. The architecture consists of a backbone neural network (NN) followed by a multilayer ($k$-layered) projection to enforce nonlinear constraints. NLPOpt-Net employs an inversion-free, modified Chambolle–Pock algorithm for rapid projection during the forward pass, leveraging local quadratic approximations of the original NLP, and uses the implicit function theorem for efficient backpropagation. Numerical experiments suggest that the projection improves solution quality by driving the predictions closer to optimality while preserving feasibility. NLPOpt-Net solves convex multiparametric QP, QCQP, and NLP problems with near zero optimality gap and constraint violations reduced to machine precision, thereby enabling a scalable approach for multiparametric programming. While a first-order Taylor approximation provides a feasible projection for convex problems, we observe that, with appropriate linearization, NLPOpt-Net can also solve nonconvex problems. While the models are trained using JAX in Pyhton, the fixed structure of the projection further allows compiling a trained model in C. The compiled models provide significant improvement in inference time. Finally, we consider a nonconvex collision-free fleet trajectory optimization problem to demonstrate the ability of NLPOpt-Net to incorporate large number of constraints.