This paper proposes a method for the solution of constrained min-max problems. The method is tested on a benchmark of representative problems presenting different structures for the objective function and the constraints. The particular min-max problem addressed in this paper finds application in optimisation under uncertainty when the constraints need to be satisfied for all possible realisations of the uncertain quantities. Hence, the algorithm proposed in this paper search for solutions that minimise the worst possible outcome for the objective function due to the uncertainty while satisfying the constraint functions in all possible scenarios. A constraint relaxation and a scalarisation procedure are also introduced to trade-off between objective optimality and constraint satisfaction when no feasible solutions can be found.

本文提出了一种约束最小-最大问题的求解方法。该方法在代表问题的基准上进行了测试，该问题针对目标函数和约束给出了不同的结构。当不确定性量的所有可能实现都需要满足约束条件时，本文解决的特定最小-最大问题将在不确定性条件下的优化中找到应用。因此，本文提出的算法寻求的解决方案是在不确定性的情况下将目标函数的最坏结果最小化，同时在所有可能的情况下都满足约束函数。当找不到可行的解决方案时，还引入了约束松弛和标量程序来在目标最优与约束满足之间进行权衡。