Inverse optimization for linearly constrained convex separable programming problems

In this paper, we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas. For a given feasible point of a convex separable program, the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem, and when the answer is positive, find the parameter values that have the smallest adjustments. A sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values. Inverse optimization formulations are presented with ℓ1ℓ1 and ℓ2ℓ2 norms. These inverse optimization problems are either linear programming when ℓ1ℓ1 norm is used in the formulation, or convex quadratic separable programming when ℓ2ℓ2 norm is used.