Abstract: In order to solve inverse quadratic programming problems effectively, a smoothing trust region Newton-CG method to solve its dual sub problem is proposed.  Augmented Lagrange method is used to solve the dual problem and then the dual sub problem is conversed into a continuous unconstrained optimization problem through introducing a smoothing function. The trust region method and the conjugate gradient method are combined to design the algorithm flow of inverse quadratic programming problems. It is proved that this method is effective by numerical experiments, and compared with Newton method, it is more suitable for solving large scale problems.

Key words: quadratic programming, inverse programming problems, smooth function, trust-region Newton-CG method

摘要： 为了有效地求解二次规划逆问题，提出了一种求解其对偶问题的子问题的光滑化信赖域共轭梯度法。该方法采用增广拉格朗日法求解其对偶问题，引入光滑函数将对偶问题的子问题转换成连续的无约束优化问题，将信赖域法与共轭梯度法结合，设计出求解二次规划逆问题的算法流程。数值实验结果表明，该方法可行且有效，与牛顿法相比，更适合求解大规模问题。

关键词: 二次规划, 逆问题, 光滑函数, 信赖域共轭梯度法