MPVCC问题的AC稳定性及算法研究

The AC-stationarity for MPVCC and algorithmic consequences

带有垂直互补约束的数学规划(MPVCC)问题是一类较难处理的优化问题.因此,通常应用专门的算法来求解MPVCC.近年来,序列最优性条件被广泛应用于算法的收敛性分析,但是非线性优化问题的序列最优性条件并不适用于MPVCC.因此,基于MPVCC的C稳定性,给出了近似C稳定性(AC稳定性),并证明了它是MPVCC的序列最优性条件.此外,还证明了在AC正则性下,AC稳定性可以保证C稳定性成立.最后,证明了MPVCC的增广拉格朗日方法生成的序列满足AC稳定性条件.

Mathematical programs with vertical complementarity constraints(MPVCC)is a difficult class of optimization problems.Therefore,it is necessary to design specialized algorithms for solving MPVCC.In recent years,the sequential optimality conditions are widely used in the analysis of convergence of algorithms for nonlinear optimization.However,they are not suitable for MPVCC.We propose a sequential optimality condition for Clarke stationarity concepts for MPVCC and we call the condition approximate Clarke stationarity(AC-stationarity).We show that the AC-stationary point satisfying the AC-regular constraint qualification is a C-stationary point.Finally,we show that the augmented Lagrangian method for MPVCC reaches AC-stationary point.