PANDA: A Matrix-Free Differentiable NMPC Solver via Proximal Averaged Quasi-Newton with Adaptive Linesearch Algorithm

What the math gives to ML

The paper offers two transferable mechanisms: a proximal, quasi-Newton forward iteration with adaptive nonmonotone stepsize enlargement, and matrix-free implicit differentiation through Krylov adjoint solves. The first can replace ordinary gradient descent in neural-network training when parameters or activations are subject to nonsmooth constraints, while the second can make deep equilibrium, differentiable optimization, and recurrent solver layers trainable without materializing Hessians or Jacobians. The strongest neural-network transfer is a constrained optimizer or solver layer whose forward residual is solved with proximal quasi-Newton steps and whose backward pass uses only automatic-differentiation vector-Jacobian and Jacobian-vector products. Both mechanisms make quantitative predictions: accepted steps should approach a local stability ceiling, and Krylov residuals should decay geometrically when the linearized residual operator is well-conditioned.