Constrained optimization is a tool for minimizing or maximizing some objective, subject to constraints. For example, we may want to build new warehouses that minimize the average cost of shipping to our clients, constrained by our budget for building and operating those warehouses. Or, we might want to purchase an assortment of merchandise that maximizes expected revenue, limited by a minimum number of different items to stock in each department and our manufacturers’ minimum order sizes.
Here’s the catch: all objectives and constraints must be linear or quadratic functions of the model’s fixed inputs (parameters, in the lingo) and free variables.
Constraints are limited to equalities and non-strict inequalities. (Re-writing strict inequalities in these terms can require some algebraic gymnastics.) Conventionally, all terms including free variables live on the lefthand side of the equality or inequality, leaving only constants and fixed parameters on the righthand side.
To build your model, you must first formalize your objective function and constraints. Once you’ve expressed these terms mathematically, it’s easy to turn the math into code and let pyomo find the optimal solution.
I haven’t touched it in a decade, but I did have some success with LINGO for solving the same type of problem.