具有补偿的两阶段随机二阶锥规划问题的一个等价形式

An equivalent form of two-stage stochastic second-order cone programming problem with recourse

确定的二阶锥规划(DSOCP)是一类凸优化问题,为处理DSOCP的数据的不确定性,具有补偿的随机二阶锥规划问题备受关注.有许多重要的实际问题,如随机欧几里得设施位置问题、具有损失风险约束的投资组合优化问题、最优覆盖随机椭球问题等均可建模为具有补偿的随机二阶锥规划问题,有效求解方法多为内点法.讨论具有补偿的随机两阶段二阶锥规划问题,在Slater约束规范条件下,探讨了第二阶段问题的对偶问题及最优值函数的次微分性质,在随机变量的概率分布具有有限支撑的条件下,给出了两阶段随机二阶锥规划问题的一个等价的线性二阶锥规划问题.

Deterministic second-order cone programs(DSOCPs)are a class of convex optimization problems.For handling uncertainty in data defining DSOCPs,Stochastic second-order cone programs(SSOCPs)with recourse have attracted much attention.There are many important practical problems,such as stochastic Euclidean facility location problem,portfolio optimization problem with loss risk constraints,optimal covering random ellipsoid problem,etc.can be modeled as stochastic second-order cone programs with recourse.Interior point method is one of the most successful classes of algorithms for solving SSOCPs.In this paper,two-stage stochastic second-order cone programming problem with recourse is discussed.Under Slater condition,dual problem of the second-stage problem is built and the subdifferential property of optimal value function is analyzed.Suppose that the probability distribution of random variables has finite support,an equivalent linear second-order cone programming problem for two-stage stochastic second-order cone programming problem is presented.