Scalable Solution Strategies for Chance-Constrained Nonlinear Programs,Industrial & Engineering Chemistry Research

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Scalable Solution Strategies for Chance-Constrained Nonlinear Programs
Industrial & Engineering Chemistry Research ( IF 3.8 ) Pub Date : 2018-06-04 , DOI: 10.1021/acs.iecr.8b00646
Javier Tovar-Facio ₁ , Yankai Cao ₂ , Jose M. Ponce-Ortega ₁ , Victor M. Zavala ₂

Affiliation

Probabilistic (chance) constraints are a powerful modeling paradigm that helps decision-makers control risk. Unfortunately, chance constraints (CCs) cannot be handled directly by off-the-shelf optimization solvers and specialized reformulations and solution procedures are often needed. In this work, we review different strategies to tackle large-scale nonlinear programs (NLPs) with CCs. In particular, we use moment matching when the algebraic structure of the moments and of the quantile function of the CC distribution are known. To address more general settings with arbitrary distributions, we use a sigmoidal approximation, which provides a mechanism to achieve exact solutions. We demonstrate that this approach significantly reduces the conservatism of popular approximations such as the conditional value at risk and the scenario (almost surely) approach. A flare system design study is used to illustrate the developments.

中文翻译：

机会约束非线性程序的可扩展解决方案策略

概率约束（机会约束）是一种强大的建模范例，可帮助决策者控制风险。不幸的是，现成的优化求解器无法直接处理机会约束（CC），并且经常需要专门的重新制定公式和求解程序。在这项工作中，我们回顾了使用CC解决大规模非线性程序（NLP）的不同策略。特别是，当矩的代数结构和CC分布的分位数函数已知时，我们使用矩匹配。为了解决具有任意分布的更一般的设置，我们使用了S形近似，它提供了一种实现精确解的机制。我们证明了这种方法大大降低了流行近似法的保守性，例如风险中的条件价值和情景（几乎可以肯定）的方法。火炬系统设计研究用于说明发展情况。

更新日期：2018-06-04

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