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Neural networks (NNs) have emerged as promising tools for solving constrained optimization problems in real-time. However, ensuring constraint satisfaction for NN-generated solutions remains challenging due to prediction errors. Existing methods to ensure NN feasibility either suffer from high computational complexity or are limited to specific constraint types.We present Bisection Projection, an efficient approach to ensure NN solution feasibility for optimization over general compact sets with non-empty interiors.Our method comprises two key components:(i) a dedicated NN (called IPNN) that predicts interior points (IPs) with low eccentricity, which naturally accounts for approximation errors;(ii) a bisection algorithm that leverages these IPs to recover solution feasibility when initial NN solutions violate constraints.We establish theoretical guarantees by providing sufficient conditions for IPNN feasibility and proving bounded optimality loss of the bisection operation under IP predictions. Extensive evaluations on real-world non-convex problems demonstrate that Bisection Projection achieves superior feasibility and computational efficiency compared to existing methods, while maintaining comparable optimality gaps.