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Ensuring solution feasibility is a key challenge in developing Deep NeuralNetwork (DNN) schemes for solving constrained optimization problems, due toinherent DNN prediction errors. In this paper, we propose a ``preventivelearning'' framework to guarantee DNN solution feasibility for problems withconvex constraints and general objective functions without post-processing,upon satisfying a mild condition on constraint calibration. Without loss ofgenerality, we focus on problems with only inequality constraints. Wesystematically calibrate inequality constraints used in DNN training, therebyanticipating prediction errors and ensuring the resulting solutions remainfeasible. We characterize the calibration magnitudes and the DNN sizesufficient for ensuring universal feasibility. We propose a newAdversarial-Sample Aware training algorithm to improve DNN's optimalityperformance without sacrificing feasibility guarantee. Overall, the frameworkprovides two DNNs. The first one from characterizing the sufficient DNN sizecan guarantee universal feasibility while the other from the proposed trainingalgorithm further improves optimality and maintains DNN's universal feasibilitysimultaneously. We apply the framework to develop DeepOPF+ for solvingessential DC optimal power flow problems in grid operation. Simulation resultsover IEEE test cases show that it outperforms existing strong DNN baselines inensuring 100% feasibility and attaining consistent optimality loss ($<$0.19%)and speedup (up to $\times$228) in both light-load and heavy-load regimes, ascompared to a state-of-the-art solver. We also apply our framework to anon-convex problem and show its performance advantage over existing schemes.

Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems