Smoothing methods for complementarity problems in process engineering
Smoothing methods for complementarity problems in process engineering
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DOI：
10.1002/aic.690450715
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发表时间：
1999-07
期刊：
影响因子：
3.7
通讯作者：
V. Gopal;L. Biegler
中科院分区：
文献类型：
--
作者：
V. Gopal;L. Biegler
互补性是所有约束优化问题的核心。然而，直接实施互补条件是困难的，因为与它们相关的固有不可微性。本文研究了用连续算法求解非线性方程组来解决互补问题的一类光滑化方法。利用具有单一光滑参数的简单函数，研究了光滑方法逼近复杂嵌套导数间断的适用性。此外，还给出了求解具有互补条件的相平衡问题的基于方程的公式。该方法可以直接模拟相平衡问题中相的出现和消失。此外，还展示了如何使用平滑方法来求解极限蒸馏情况，例如干塔板和无汽塔板，在基于方程的公式中建模。
Complementarity is central to all constrained optimization problems. However, direct enforcement of complementarity conditions is difficult because of the inherent nondifferentiability associated with them. Here, a class of smoothing methods for solving the complementarity problem by using a continuation algorithm to solve nonlinear equations is studied. The applicability of smoothing methods to approximate complicated nested derivative discontinuities is investigated using simple functions with a single smoothing parameter. In addition, an equation-based formulation for solving the phase equilibrium problem with complementarity conditions is formulated. This approach can model the appearance and disappearance of phases directly in phase equilibrium problems. Moreover, it is shown how smoothing methods can be used to solve limiting distillation cases, such as dry and vaporless trays, modeled within an equation-based formulation.