A Perturbation Approach For A Class Of Inverse Linear Programming Problems

An optimization model, usually involves parameters associated with decision variables in the objective function or in the constraint set. The forward optimization problem is to find optimal solutions to the optimization model in which parameter values are known. However, there are many instances in the practice, in which we only know some estimates for parameter values, but we may have certain optimal solutions from our experience, observations or experiments. An inverse optimization problem is to find values of parameters which are near to the given estimates and make the known solutions optimal. This dissertation focuses on studying a perturbation method for a class of inverse linear programming problems.The main results, obtained in this dissertation, may be summarized as follows:1. In chapter 2, we introduce some results from semi-smooth analysis which are needed in convergence analysis. We also introduce the concept of Lagrange duality and KKT system.2. In chapter 3, we devote to reformulating the inverse linear programming problem as a linear complementary constrained optimization problem.3. In chapter 4, we propose a new perturbation way to solve this inverse problem.4. In chapter 5, we propose the semi-smooth Newton method to solve the equations. And we prove the local convergence and the global convergence of this method.5. In chapter 6, numerical experiments are reported to verify the effectiveness of the method.