A Smoothing Newton Method For A Type Of Inverse Quadratic Programming Problems With Second Order Cone Constraints

In practice, we often encounter the situations in which it is difficult to give the precise parameters associated with decision variables in the objective function, even the programming model has been established in a clear formulation, whereas we can find the optimal solution by experience or experiments, we hope to get satisfactory resulst by adjusting the parameters as little as possible. This is just a so-called inverse problem. As the optimization inverse problems have wide applications in many fields, it gradually attracts the attentions from scholars in recent years. But for continuous optimization, except for linear programming, we do not see much deep study on their inverse problems. Therefore, our concern is an inverse quadratic programming problem with second order cone constraint, which is a specific inverse problem in continuous optimization. Using the smoothing Newton method, this paper solves the KKT system of the dual problem of the inverse quadratic programming problem with second order cone constraint. It gives the theoretic analysis of the smoothing Newton method, including the global convergence and local convergence rate. Furthermore, Numerical experiments are reported to show that the smoothing Newton method is effective for solving the type of inverse quadratic programming problems. The main results in this paper can be generalized as follow:1. Chapter 2 introduces some results from nonsmooth analysis which shall be used in our convergence analysis.2. Using the results from the reference, Chapter 3 derives the expressions of the inverse and dual form of the quadratic programming problem with second order cone constraint, and establishes the KKT system of the dual problem.3. In Chapter 4, a smoothing Newton method is suggested for solving the smoothing KKT system.4. Chapter 5 shows that the algorithm in Chapter 4 has global convergence and the quadratic convergence rate.5. Chapter 6 reports numerical experiments to verify the effectiveness of the proposed method..