Optimality-Aware Projection: Aligning Projection Geometry with Constrained Optimization

In learning-based constrained optimization pipelines, feasibility-enforcement layers are widely adopted to guarantee strict constraint satisfaction. However, optimizing an unconstrained loss through such feasibility mappings creates a non-equivalent surrogate formulation for the target constrained optimization problem. Specifically, methods based on orthogonal projection exhibit boundary-collapse behavior, which suppresses gradient components normal to active constraints. Consequently, stationary points of this surrogate formulation misalign with the optimality conditions of the target problem, driving convergence to suboptimal solutions. To address this issue, we propose Optimality-Aware (OA) projection , a novel learning mechanism that endows projection-integrated architectures with genuine optimality-seeking capabilities. Without modifying the orthogonal projection layer itself, OA projection injects a KKT-residual-guided geometric correction into the training gradient flow, making it readily embedded into learning-based optimization pipelines. By recovering informative gradients that propel optimization progress along boundaries, this correction favorably reshapes the parameter trajectory and systematically avoids orthogonal-projection-induced spurious stationary points. Theoretically, we establish the differentiability of OA projection, prove its convergence under stochastic gradient updates, and show that under suitable regularity conditions, the converged iterates satisfy the KKT conditions of the target problem. Experimental results on diverse benchmarks, including real-world tasks, confirm that OA projection outperforms state-of-the-art methods by substantially improving the solution quality of hard-constrained learning models while strictly preserving feasibility.