Allocation and management of agricultural land is of emergent concern due to land scarcity, diminishing supply of energy and water, and the increasing demand of food globally. To achieve social, economic and environmental goals in a specific agricultural land area, people and society must make decisions subject to the demand and supply of food, energy and water (FEW). Interdependence among these three elements, the Food-Energy-Water Nexus (FEW-N), requires that they be addressed concertedly. Despite global efforts on data, models and techniques, studies navigating the multi-faceted FEW-N space, identifying opportunities for synergistic benefits, and exploring interactions and trade-offs in agricultural land use system are still limited. Taking an experimental station in China as a model system, we present the foundations of a systematic engineering framework and quantitative decision-making tools for the trade-off analysis and optimization of stressed interconnected FEW-N networks. The framework combines data analytics and mixed-integer nonlinear modeling and optimization methods establishing the interdependencies and potentially competing interests among the FEW elements in the system, along with policy, sustainability, and feedback from various stakeholders. A multi-objective optimization strategy is followed for the trade-off analysis empowered by the introduction of composite FEW-N metrics as means to facilitate decision-making and compare alternative process and technological options. We found the framework works effectively to balance multiple objectives and benchmark the competitions for systematic decisions. The optimal solutions tend to promote the food production with reduced consumption of water and energy, and have a robust performance with alternative pathways under different climate scenarios.