A new flexibility index algorithm for systems under uncertainty and represented by quadratic inequalities is presented. Inspired by the outer‐approximation algorithm for convex mixed‐integer nonlinear programming, a similar iterative strategy is developed. The subproblem, which is a nonlinear program, is constructed by fixing the vertex directions since this class of systems is proved to have a vertex solution if the entries on the diagonal of the Hessian matrix are non‐negative. By overestimating the nonlinear constraints, a linear min–max problem is formulated. By dualizing the inner maximization problem, and introducing new variables and constraints, the master problem is reformulated as a mixed‐integer linear program. By iteratively solving the subproblem and master problem, the algorithm can be guaranteed to converge to the flexibility index. Numerical examples including a heat exchanger network, a process network, and a unit commitment problem are presented to illustrate the computational efficiency of the algorithm. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2486–2499, 2018

中文翻译：

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二次系统柔性指标问题的新算法

提出了一种新的系统不确定性指标指数算法，该算法以二次不等式表示。受凸混合整数非线性规划的外逼近算法启发，开发了类似的迭代策略。该子问题是一个非线性程序，它是通过固定顶点方向来构造的，因为如果Hessian矩阵对角线上的项为非负值，则证明此类系统具有顶点解。通过高估非线性约束条件，提出了线性最小-最大问题。通过将内部最大化问题对偶化，并引入新的变量和约束，将主问题重新构造为混合整数线性程序。通过迭代解决子问题和主问题，可以保证算法收敛到灵活性指标。给出了包括热交换器网络，过程网络和机组承诺问题在内的数值示例，以说明该算法的计算效率。©2018美国化学工程师学会AIChE J，64：2486–2499，2018年