具有离散分布的两阶段随机二阶锥规划问题的最优性条件

Optimality conditions for two-stage stochastic second-order cone programming problems with discrete distribution

两阶段随机二阶锥规划模型在工程和生产等许多实际问题中有广泛的应用,该模型的有效求解方法备受关注.最优性条件在算法设计中扮演着重要的角色.基于Lagrange对偶理论,主要探讨具有离散分布的两阶段随机二阶锥规划问题的最优性条件.在Slater条件下,建立了第二阶段问题的对偶问题并分析了最优值函数的次微分性质;当随机数据服从离散分布时,证明了两阶段随机二阶锥规划问题的最优性条件.

The two-stage stochastic second-order cone programming model has been widely used in many practical problems such as engineering and production. The effective methods for solving this model have attracted much attention. It is well known that optimality conditions play an important role in algorithm design. Based on Lagrange duality theory, the optimality condition for two-stage stochastic second-order cone programming problem with discrete distribution are dicussed. Under the Slater condition, the dual problem of the second-stage problem is established and the subdifferential property of the optimal value function is analyzed.When the random data obey the discrete distribution, the optimality condition of the two-stage stochastic second-order cone programming problem is proved.