Learning based convex approximation for constrained parametric optimization
This work addresses optimization problems in domains like power systems, offering a novel learning-based method that improves upon existing solvers and learning approaches, though it is incremental in combining known techniques.
The paper tackles continuous constrained optimization problems by proposing an ICNN-based self-supervised learning framework integrated with ALM and constraint correction, achieving non-strict constraint feasibility, better optimality gap, and best convergence rate compared to state-of-the-art methods, with superior accuracy, feasibility, and computational efficiency on benchmarks like QP and AC optimal power flow.
We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism, our framework ensures \emph{non-strict constraint feasibility}, \emph{better optimality gap}, and \emph{best convergence rate} with respect to the state-of-the-art learning-based methods. We provide a rigorous convergence analysis, showing that the algorithm converges to a Karush-Kuhn-Tucker (KKT) point of the original problem even when the internal solver is a neural network, and the approximation error is bounded. We test our approach on a range of benchmark tasks including quadratic programming (QP), nonconvex programming, and large-scale AC optimal power flow problems. The results demonstrate that compared to existing solvers (e.g., \texttt{OSQP}, \texttt{IPOPT}) and the latest learning-based methods (e.g., DC3, PDL), our approach achieves a superior balance among accuracy, feasibility, and computational efficiency.