Pyomo v4.1 is an extensible software platform for developing optimization-based analytics to support complex decision-making in real-world applications. Optimization—finding a solution that minimizes (or maximizes) a function over a set of possible alternatives—is widely used in business, science, and engineering to minimize costs, identify worst-case scenarios, and analyze trade-offs. Optimization is used to: schedule commercial aircraft and crews; manage supply chains for auto manufacturers; select investment portfolios on Wall Street; design sensor networks to protect water distribution systems; identify locations for military supply depots; design sport schedules for Major League Baseball and operate power grids worldwide. Optimization is also the computational engine behind many statistical and machine-learning techniques used for data analysis. Complex, real-world optimization problems require the use of modeling languages (MLs), sophisticated tools that simplify the process of describing and analyzing optimization problems. Specifically, MLs are applied to develop an optimization model or a high-level description of an optimization problem.