A Trust-region Newton-CG Method For Inverse Quadratic Programming Problems

The paper introduces the background and research status of inverse optimizationproblems, and then proposes the inverse problems for a class of quadratic programmingthat the paper studied. The kind of inverse problems makes the known feasible solutionbe the optimal solution of the problem adjusted by fine-tuning of the parameter matrixof the objective function of quadratic programming. In order to solve the inverseproblem of quadratic programming and reduce the complexity of the problem, firstly theoriginal problem can be transformed into the dual problem. Secondly, the dual problemis solved by using the general augmented Lagrange method, and then proves the globalconvergence of the algorithm and the feasibility under certain assumption conditions. Atlast, use the smoothing trust region Newton-CG method that proposed in this paper tosolve the sub-problem of the dual problem. The method transforms the sub-problem ofthe dual problem into a continuous unconstrained optimization problem by introducing asmoothing function. Finally, the algorithm of solving the inverse problem of quadraticprogramming has been designed, combining the advantages of the trust region methodand conjugate gradient method. At last, the numerical and experimental results showthat the proposed algorithm is more effective and more suitable for large-scale problemsthan Newton method.