The Study For A Class Of An Inverse Quadratic Programming Problem

In an optimization model, usually there are parameters associated with decision variables inthe objective function or in the constraint set. When solving the optimization problem, weusually assume that these parameter values are known in order to solve optimal solution forthe known optimization model. However, there are many instances in the practice, in whichwe only know some estimates for parameter values, but we may have certain optimalsolutions from experience, observations or experiments. An inverse optimization problem isto find values of parameters which make the known solutions optimal and which differ fromthe given estimates as little as possible. Our mainly studying is on a class of inverse quadraticprogramming problem in this dissertation.The main results, obtained in this dissertation, may be summarized as follows:1. In chapter 2, we give some conclusions for semi-smoothing analysis, this will do help forconvergence. We also introduce the concept of Lagrange duality and KKT system.2. With the help of the related results of [1], Chapter 3 is devoted to reformulating theinverse quadratic programming problem as a linear complementarity constrainedoptimization problem, namely IQP(A) which has a SC~1 convex objective function andfewer decision variables than the original inverse quadratic problem. We also give somegeneral properties of the metric projector.3. Different from the perturbation approach proposed in [1], in chapter 4, we propose a newperturbation way to solve problem IQP(A). We introduce the concept of C-stationarypoints and show that any limit point of solutions to perturbation problems is a C-stationarypoint. Finally, we use smoothing Newton method to solve the auxiliary equations andprove the global convergence of the smoothing Newton method.