本文探讨了鲁棒优化和随机规划两种处理不确定性的优化方法。鲁棒优化针对不确定参数不使用概率分布描述的情况，寻求在不确定性集合内所有可能实现下都可行且最优化的解决方案。对比之下，随机规划通过定义可能发生的情景及其概率来解决不确定性问题，并分为两阶段问题，第一阶段决策不依赖于随机变量的实际值，而第二阶段决策则基于已知的不确定性参数。文章还讨论了这两种方法的优点与局限。
1. Robust optimization addresses optimization problems with uncertain parameters that are not described using probability distributions but uncertainty sets.
2. A robust optimization problem seeks to determine a solution to an optimization problem that is feasible for any realization of the uncertain parameters within the uncertainty set, and optimal for the worst-case realization
of these uncertain parameters.
a stochastic programming problem 的缺点：
(1) the number of scenarios太多，导致问题规模增大
(2) distribution functions很难描绘不确定变量的特性
Robust Optimization优点：
computationally efficient and modelling flexibility
代价：At the cost of reduced flexibility
可以用对偶变换来变成 single-level的问题来求解，但一个重要前提是最里层的优化问题是convex的
对比：
Stochastic：
Random vector λ is then modeled as a set Ω of plausible outcomes or scenarios
ω, where each ω ∈ Ω has an associated probability of occurrence πω such that
ω∈Ω πω = 1.
Stochastic Programming Problems with Recourse
The simplest recourse problem is the two-stage stochastic programming problem,
in which decisions are divided into two groups, namely:
• Decisions that have to be made before the realization of uncertain parameters：
first-stage or here-and-now decisions and do not depend on the realization of the random parameters. 联系动态经济调度中，t=1时的优化叫first-stage，变量叫 here-and-now decision variables。
• Decisions that are made after the actual values of uncertain parameters are
disclosed.
“second-stage, wait-and-see, or recourse decisions”
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