二次规划逆问题的牛顿方法

针对二次规划逆问题,将其表达为带有互补约束的锥约束优化问题.借助于对偶理论,将问题转化为变量更少的线性互补约束非光滑优化问题.通过扰动的方法求解转化后的问题并证明了收敛性.采用非精确牛顿法求解扰动问题,给出了算法的全局收敛性与局部二阶收敛速度.最后通过数值实验验证了该算法的可行性.

Newton methods for inverse problems of quadratic programming

This paper is devoted to the study of the inverse quadratic program- ming. The problem can be formulated as a cone constrained optimization problem with a complementary constrain. Based on the theory of duality, we reformulate this prob- lem as a linear complementarity constrained nonsmooth optimization problem with fewer variables than the original one. We introduce a perturbation approach to solve the refor- mulated problem and demonstrate the global convergence. An inexact Newton method is constructed to solve the perturbation problem and its global convergence and local quadratic rate can be obtained. In the end, our numerical experiment results show the feasibility of this method.