Inverse linear optimization for the recovery of constraint parameters in robust and non-robust problems

Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem. In this thesis, we propose two approaches to impute unspecified left-hand-side constraint coefficients in addition to a cost vector for a given linear optimization problem. The ďŹ rst approach minimally perturbs prior estimates of the unspecified parameters to satisfy strong duality, while the second identifies parameters minimizing the duality gap, if it is not possible to satisfy the optimality conditions exactly. We apply these two approaches to the general linear optimization problem. We also use them to impute unspecified parameters of the uncertainty set for robust linear optimization problems under interval and cardinality constrained uncertainty. Each inverse optimization model we propose is nonconvex, but we show that a globally optimal solution can be obtained by solving a ďŹ nite number of tractable optimization problems.M.A.S