Duality for Stochastic Programming Interpreted as L. P. in $L_p $-Space
Duality for Stochastic Programming Interpreted as L. P. in $L_p $-Space
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随机规划的对偶性解释为 $L_p $-Space 中的 L. P.
DOI：
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发表时间：
1975
期刊：
影响因子：
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通讯作者：
Paul Olsen
中科院分区：
文献类型：
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作者：
M. Eisner;Paul Olsen
将线性约束多阶段随机规划问题解释为$L_p $-空间中的规划问题，如果随机问题是线性的，则该问题是线性的，并根据Rockafellar[16]的一般结果建立了对偶理论。对线性问题的对偶性是对称的，只要随机模型得到适当的推广，并且可以给出经济解释。如果与扰动函数题词密切相关的某集$mathcal{C}$是闭合的，则随机规划问题达到其最小值，该最小值等于对偶问题的最优值。$mathcal{C}$的封闭性来自于问题的技术矩阵A上的简单条件。
The linearly constrained multistage stochastic programming problem is interpreted as a programming problem in $L_p $-space, linear if the stochastic problem is linear, and a duality theory is developed from the general results of Rockafellar [16]. The duality is symmetric for linear problems, provided that the stochastic model is suitably generalized, and can be given an economic interpretation. If a certain set $mathcal{C}$, closely related to the epigraph of the perturbation function, is closed, then the stochastic programming problem attains its minimum, which equals the supremum of the dual problem. The closedness of $mathcal{C}$ follows from simple conditions on the technology matrix A for the problem.