Inverse optimization problems: modeling of parameters of lower (upper) bounds and parameters of the objective function
The statement of the problem is given in the first part and the description of its parameters. The second part is devoted to modeling of the parameters for the constraints (lower and upper bounds) in accordance with the selected norm. As a result of solving the inverse optimization problem to change the lower and upper bounds in accordance with the selected norm the infeasible solution becomes the feasible solution. In the third part of the work a numerical example of modeling parameters of the lower and upper bounds is considered. In the fourth part of this work the mathematical model of the inverse optimization problem for modeling parameters of the objective function is considered. As a result of solving the inverse optimization problem the new parameters of the objective function are obtained. For the new parameters of the objective function the feasible solution of the direct problem becomes its optimal solution. In the final part of the work a numerical example of modeling parameters of the objective function in accordance with the selected norm is considered. The results can be used to solve linear optimization problems in networks when the parameters of the lower and upper bounds and the parameters of the objective function are unknown.