Inferring linear feasible regions using inverse optimization

Consider a problem where set of feasible observations are provided by an expert and cost function is defined that characterizes which the dominate others hence, preferred. Our goal to find linear constraints would render all given while making preferred ones optimal for (objective) function. By doing so, we infer implicit region programming problem. Providing such regions (i) builds baseline categorizing future as or infeasible, (ii) allows using sensitivity analysis discern changes in solutions if objective future. In this paper, propose inverse optimization framework recover forward multiple past input. We focus on models known but constraint matrix partially fully unknown. general methodology recovers complete then introduce tractable equivalent reformulation. Furthermore, provide discuss several generalized loss functions inform desirable properties based user preference historical data. numerical examples verify validity our approach, emphasize differences among proposed measures, intuition large-scale implementations. further demonstrate approach diet recommendation show how can help impute personalized each dieter.