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A New Theoretical Framework for Robust Optimization Under Multi-Band Uncertainty

机译：多频段不确定性下的鲁棒优化的新理论框架

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1 Introduction A central assumption in classical optimization is that all parameters describing the problem are known exactly. However, many real-world problems consider data that are uncertain or not known with precision (for example, because of measurement methodologies which introduce an error or because of approximated numerical representations). Neglecting the uncertainty may have dramatic effects and turn optimal solutions into infeasible or very costly solutions. Since the groundbreaking investigations by Dantzig [11], many works have thus tried to find effective ways to deal with uncertainty (see [2] for an overview). During the last years, Robust Optimization (RO) has attracted a lot of attention as a valid methodology to deal with uncertainty affecting optimization problems. A key feature of RO is to take into account uncertainty as hard constraints, which are added to the original formulation of the problem in order to cut off solutions that are not robust, i.e. protected from deviations of the data. For an exhaustive introduction to the theory and applications of RO, we refer the reader to the book by Ben-Tal et al. [1], to the recent survey by Bertsimas et al. [2] and to the Ph.D. Thesis [6].
机译：1引言经典优化中的中央假设是描述问题的所有参数都是完全清楚的。然而，许多现实世界问题考虑了精确度或不知道的数据（例如，因为导致误差或由于近似的数值表示）的测量方法。忽视不确定性可能具有戏剧性的效果，并将最佳解决方案变为不可行或非常昂贵的解决方案。由于Dantzig的突破性调查[11]，因此许多作品试图找到处理不确定性的有效方法（见[2]概述）。在过去几年中，强大的优化（RO）吸引了很多关注，作为处理影响优化问题的不确定性的有效方法。 RO的一个关键特征是考虑不确定性作为硬约束，这被添加到问题的原始制定中，以便切断不稳健的解决方案，即保护免受数据的偏差。为了彻底介绍RO的理论和应用，我们将读者通过Ben-tal等人推荐给这本书。 [1]，到最近的Bertsimas等。 [2]和博士。论文[6]。

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