Inferring linear feasible regions using inverse optimization

•Inverse optimization models are proposed to infer the complete feasible region of an LP.•One or multiple observed solutions are considered as input to the inverse model.•A tractable linearly-constrained equivalent reformulation is proposed for solving the bilinear inverse problem.•Generalized loss functions for inducing the desirable properties of the imputed feasible region are introduced.•The applicability of the approach is demonstrated through a a diet recommendation case study.