Constrained Bundle Methods for Upper Inexact Oracles with Application to Joint Chance Constrained Energy Problems
Constrained Bundle Methods for Upper Inexact Oracles with Application to Joint Chance Constrained Energy Problems
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DOI：
10.1137/120903099
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发表时间：
2014-04
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影响因子：
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通讯作者：
W. Ackooij;C. Sagastizábal
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文献类型：
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作者：
W. Ackooij;C. Sagastizábal
联合机会约束问题带来了许多算法上的挑战。即使在凸情形下，即当概率约束的适当变换是一个凸函数时，其割平面线性化也只是一种近似，它是由一个神谕（oracle）产生的，该神谕提供的次梯度和函数值只能不精确地计算。因此，割平面模型可能位于真实约束之上。为了处理这种上不精确神谕，并且仍然将问题求解到一定精度，必须采用一种特殊的数值算法。我们引入了一类基于所谓改进函数的约束束方法，这类方法被证明是收敛的，并且包含了许多先前的方法以及新的算法。根据神谕的准确性，我们分析了所考虑的方法在多大程度上解决了联合机会约束规划问题。该方法在处理随机水库管理时出现的实际能源问题上进行了评估。
Joint chance constrained problems give rise to many algorithmic challenges. Even in the convex case, i.e., when an appropriate transformation of the probabilistic constraint is a convex function, its cutting-plane linearization is just an approximation, produced by an oracle providing subgradient and function values that can only be evaluated inexactly. As a result, the cutting-plane model may lie above the true constraint. For dealing with such upper inexact oracles, and still solving the problem up to certain precision, a special numerical algorithm must be put in place. We introduce a family of constrained bundle methods, based on the so-called improvement functions, that is shown to be convergent and encompasses many previous approaches as well as new algorithms. Depending on the oracle accuracy, we analyze to what extent the considered methods solve the joint chance constrained program. The approach is assessed on real-life energy problems, arising when dealing with stochastic hydroreservoir management.