AI-Blockchain Framework for Nonconvex Equilibrium in Sustainable Agri-Food Supply Chains

This study aims to overcome critical inefficiencies in sustainable supply chains caused by nonconvex constraints such as discrete carbon tax thresholds and regulatory discontinuities that render traditional convex optimization models inapplicable. The primary objective is to establish a rigorous mathematical foundation for trifunctional multivalued equilibrium problems in non-convex Hausdorff topological spaces and to operationalize it through a practical AI-blockchain integration for agri-food logistics. Methods include proving existence theorems for EP1 and EP2 using novel finite-cycle conditions, closedness, and diagonal properties without convexity assumptions, followed by the development of the Cycle-Breaking Iterative Algorithm (CBIA) that incorporates Tikhonov regularization for stability against AI predictive errors and grid-based enumeration for polynomial-time convergence. Analysis is performed on a 160-node Vietnam rice and cashew supply chain model with blockchain-enforced emission bands and AI-predicted demand intervals. Findings demonstrate that the framework achieves a 37.5% simultaneous reduction in carbon emissions and post-harvest waste by enabling strategic shifts to high-compliance modes, with Monte Carlo simulations confirming robustness (mean reductions 36.8% and 37.1%, 95% CI within ±1%). The novelty lies in the first provision of existence results and a constructive cycle-breaking algorithm for nonconvex trifunctional multivalued equilibria, bridging theoretical gaps in equilibrium theory with scalable engineering solutions that advance SDG 9 (Industry, Innovation, and Infrastructure) and SDG 12 (Responsible Consumption and Production) in real-world circular economies.