A min-sum controllable risk problem, defined on a given set of elements or on combinatorial structures, which are either paths of a directed acyclic graph or spanning trees of an undirected graph, with resource-dependent risk functions of the elements, is studied. The resource amount is limited, and the objective is to distribute it between the selected elements or elements of the selected structure so that the total risk is minimized. A reduction to a series of easier problems is suggested. Solution approaches based on this reduction are asymptotically faster than the solution approaches suggested in the literature for special cases of this problem.

中文翻译：

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具有相同取值范围的凹风险函数的最小和可控风险问题

研究了一个最小和可控风险问题，定义在给定的一组元素或组合结构上，这些结构要么是有向无环图的路径，要么是无向图的生成树，具有元素的资源依赖风险函数。资源量是有限的，目标是将其分配在选定的元素或选定结构的元素之间，使总风险最小化。建议减少一系列更简单的问题。基于这种减少的解决方法比文献中针对此问题的特殊情况建议的解决方法渐近地更快。