MANIFEST: Manifold-Informed Learning of Feasibility-Enforcing Neural Solvers for Constrained Optimization

Efficient solution of parametric and nonlinear optimization problems is important in several engineering applications. Neural network surrogates have emerged as a promising alternative to traditional optimization solvers in real-time applications where fast solutions are necessary. However, ensuring constraint satisfaction, especially with equality constraints, remains a key challenge in neural solvers. We address this by introducing MANIFEST, a Manifold-Informed Feasibility Enforcement Strategy, that directly incorporates the geometry of the equality-constraint manifold into neural surrogate training, thus guiding the learned neural map toward the feasible manifold before any correction is applied. Specifically, we design a training objective that integrates optimality, distance of the predictions from the feasible manifold, and first-order information about the local geometry and parametric variation of the feasible manifold, followed by a differentiable restoration step. In contrast to existing approaches that rely on post-prediction projection or restoration for constraint enforcement, MANIFEST trains the learned map itself to remain close to the feasible manifold, thereby avoiding substantial post-prediction corrections and associated numerical issues from projections in challenging optimization landscapes. We evaluate our framework on quadratically constrained quadratic programs (QCQPs), nonlinear programs (NLPs), and nonconvex nonlinear AC optimal power flow (AC-OPF). Across these problems, MANIFEST consistently outperforms state-of-the-art approaches, achieving near-optimal solution with negligible equality and inequality violations even without correction, with subsequent restoration further reducing violation residuals to numerical zero.