Constraint Boundary Wandering Framework: Enhancing Constrained Optimization With Deep Neural Networks

Constrained optimization problems are pervasive in various fields, and while conventional techniques offer solutions, they often struggle with scalability. Leveraging the power of deep neural networks (DNNs) in optimization, we present a novel learning-based approach, the Constraint Boundary Wandering Framework (CBWF), to address these challenges. Our contributions include introducing a boundary wandering strategy inspired by the active-set method, enhancing equality constraint feasibility, and treating the Lipschitz constant as a learnable parameter. Additionally, we evaluate the regularization term, illustrating that the nonsmooth L2 norm yields superior results. Extensive testing on synthetic datasets and the ACOPT dataset demonstrates CBWF's superiority, outperforming existing deep learning-based solvers in terms of both objective and constraint loss.