| 王 炜，李忠伟*，王丹丹.两阶段随机线性优化问题的等价形式[J].海南师范大学学报自科版,2020,33(2):187-191 |
| 两阶段随机线性优化问题的等价形式 |
| An Equivalent Form of Two-stage Stochastic Linear Optimization Problem |
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| DOI：10.12051/j.issn.1674-4942.2020.02.011 |
| 中文关键词: 极小极大两阶段随机线性优化问题 风险 半定优化 |
| 英文关键词: minimax two-stage stochastic optimization problem risk semidefinite optimization |
| 基金项目:国家自然科学基金资助项目（11671184） |
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| 中文摘要: |
| 在极小极大两阶段随机线性优化问题中，往往只知道随机变量的概率分布所满足的一
些条件，并不能精确求得。文章假设随机变量的一阶矩和二阶矩是已知的，将最坏情况下的条件
风险值（CVaR）作为效用函数，基于矩理论和对偶理论，最终将概率分布由一阶矩和二阶矩描述的
极小极大两阶段随机线性优化问题转换为可求解的半定优化问题。 |
| 英文摘要: |
| This paper mainly studied the minimax two-stage random linear optimization problem. The probability distribu‐
tion of random variables often cannot be obtained accurately, only some conditions met by the probability distribution are
known. In order to solve this problem, we considered that the first moment and the second moment of random variables are
known. To make the model of the problem more realistic, a convex utility function is usually used for considering risk. In
this paper, the worst-case conditional value at risk (CVaR) was taken as the utility function. Therefore, for the minimax
two-stage stochastic linear optimization problem whose probability distribution is described by the first and second mo‐
ments, the problem can be transformed into a solvable semidefinite optimization problem through the theory of moments and
duality. |
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