不等式约束随机非线性规划的扰动Karush-Kuhn-Tucker系统的解路径

论文聚焦概率测度发生扰动时的随机非线性规划的稳定性分析的研究.目标函数的Lipschitz连续性和可行集值映射的度量正则性条件可保证最优解集合的外半连续性和最优值的Lipschitz连续性.更重要地,本文证明了,如果原问题的极小点处线性无关约束规范和强二阶充分性条件成立,那么存在一Lipschitz连续的解路径满足扰动问题的Karush-Kuhn-Tucker条件.

Solution Path of the Perturbed Karush-Kuhn-Tucker System for Stochastic Nonlinear Programming with Inequality Constraints

This paper focuses on the study for the stability of stochastic nonlinear programming when the probability measure is perturbed. Under the Lipschitz continuity of the objective function and metric regularity of the feasible set-valued mapping, the outer semicontinuity of the optimal solution set and Lipschitz continuity of optimal values are guaranteed. Importantly, it is proved that, if the linear independence constraint qualification and strong second-order sufficient condition hold at a local minimum point of the original problem, there exists a Lipschitz continuous solution path satisfying the Karush-Kuhn-Tucker conditions.