Inferring Linear Feasible Regions using Inverse Optimization

Understand

Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred.

• Our goal is to find a set of linear constraints that would render all the given observations feasible while making the preferred ones optimal for the cost (objective) function.
• By doing so, we infer the implicit feasible region of the linear programming problem.
• Providing such feasible regions (i) builds a baseline for categorizing future observations as feasible or infeasible, and (ii) allows for using sensitivity analysis to discern changes in optimal solutions if the objective function changes in the future.