STOCHASTIC CONVEX PROGRAMMING: SINGULAR MULTIPLIERS AND EXTENDED DUALITY SINGULAR MULTIPLIERS AND DUALITY
STOCHASTIC CONVEX PROGRAMMING: SINGULAR MULTIPLIERS AND EXTENDED DUALITY SINGULAR MULTIPLIERS AND DUALITY
复制标题
随机凸规划：奇异乘数和扩展对偶性 奇异乘数和对偶性
DOI：
--
复制
发表时间：
1976
期刊：
影响因子：
--
通讯作者：
R. Wets
中科院分区：
文献类型：
--
作者：
R. Rockafellar;R. Wets
本文研究了一个带补偿的两阶段随机规划问题，它是在一个扩展的拉格朗日函数中，允许某些乘子是对偶空间（i？00）*，而不是一个空间。这样的乘子可以分解为i^-分量和“奇异”分量。推广使得有可能的特征的解决方案的问题的鞍点，如果问题是严格可行的。对基本对偶框架的Kuhn-Tucker条件进行了修正，使其允许奇异乘子的存在.证明了扩展对偶问题中的最优乘子向量至少在一个广义情形下是基本对偶问题中乘子向量序列最大化的理想极限。
A two-stage stochastic programming problem with recourse is studied here in terms of an extended Lagrangian function which allows certain multipliers to be elements of a dual space (i?00)*, rather than an ϊ£λ space. Such multipliers can be decomposed into an i^-component and a "singular" component. The generalization makes it possible to characterize solutions to the problem in terms of a saddle-point, if the problem is strictly feasible. The Kuhn-Tucker conditions for the basic duality framework are modified to admit singular multipliers. It is shown that the optimal multiplier vectors in the extended dual problem are, in at least one broad case, ideal limits of maximizing sequences of multiplier vectors in the basic dual problem.