多级随机线性规划的单割和带割选择的多割SDDP：收敛性证明和数值试验
Single cut and multicut SDDP with cut selection for multistage stochastic linear programs: convergence proof and numerical experiments
摘要：
我们介绍了一个变种的多割分解算法（MuDA），称为CuSMuDA（切割选择多割分解算法），用于解决多级随机线性规划，采用了一类切割选择策略，以选择最相关的削减近似追索函数。这个类包含一级和有限内存一级切割选择策略，最初分别为随机对偶动态规划（SDDP）和对偶动态规划（DDP）引入。我们证明了该方法在有限次迭代中的几乎必然收敛，并作为副产品得到了SDDP结合我们的割选择策略在有限次迭代中的几乎必然收敛.我们比较性能的MuDA，SDDP，和他们的变种切割选择（使用1级和有限的内存1级）的投资组合问题和库存问题的几个实例。在这些实验中，一般来说，SDDP更快（即，满足停止标准更快）比MuDA和切割选择允许我们减少计算量，有限内存级别1比级别1更有效（有时更有效）。
英文摘要：
We introduce a variant of Multicut Decomposition Algorithms (MuDA), called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates a class of cut selection strategies to choose the most relevant cuts of the approximate recourse functions. This class contains Level 1 and Limited Memory Level 1 cut selection strategies, initially introduced for respectively Stochastic Dual Dynamic Programming (SDDP) and Dual Dynamic Programming (DDP). We prove the almost sure convergence of the method in a finite number of iterations and obtain as a by-product the almost sure convergence in a finite number of iterations of SDDP combined with our class of cut selection strategies. We compare the performance of MuDA, SDDP, and their variants with cut selection (using Level 1 and Limited Memory Level 1) on several instances of a portfolio problem and of an inventory problem. On these experiments, in general, SDDP is quicker (i.e., satisfies the stopping criterion quicker) than MuDA and cut selection allows us to decrease the computational bulk with Limited Memory Level 1 being more efficient (sometimes much more) than Level 1.
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