均衡约束为二阶锥约束广义方程的数学规划问题的二阶充分条件

摘要

In this paper, we consider a class of mathematical programs governed by second-order cone constrained generalized equations. We define the critical cone in terms of the directional derivative of a nonsmooth mapping and derive its equivalent characterization at a feasible point. With the help of the critical cone,we propose a set of second order sufficient conditions for the mathematical program governed by second-order cone constrained generalized equations. We demonstrate,under some conditions, that the set of second order sufficient conditions is sufficient for the second order growth of an M-stationary point.%本文考虑一类均衡约束为二阶锥约束广义方程的数学规划问题.我们通过一个非光滑映射的方向导数,给出了临界锥的定义,并建立它在可行点处的等价形式.基于此临界锥,我们提出了均衡约束为二阶锥约束广义方程的数学规划问题的二阶充分性条件,并且验证了在适当的条件下,M-稳定点处的二阶充分性条件是二阶增长条件成立的充分条件.