非线性互补约束均衡问题的一个SQP算法

An SQP Algorithm for Mathematical Programs With Nonlinear Complementarity Constraints

提出了一个求解非线性互补约束均衡问题(MPCC)的逐步逼近光滑SQP算法.通过一系列光滑优化来逼近MPCC.引入l1精确罚函数,线搜索保证算法具有全局收敛性.进而,在严格互补及二阶充分条件下,算法是超线性收敛的.此外,当算法有限步终止,当前迭代点即为MPEC的一个精确稳定点.

A successive approximation and smooth SQP method for mathematical programs with nonlinear complementarity constraints （MPCC） is described. A class of smooth programs to approximate the MPCC was introduced. Using an ll penalty function, the line search assures the global convergence, while superlinear convergence rate is shown under strictly complementary conditions and the second order sufficient condition. Moreover, it was proved that the current iterated point is an exact stationary point of the MPEC when the algorithm terminates finitely.