Chance constrained optimization of elliptic PDE systems with a smoothing convex approximation
Chance constrained optimization of elliptic PDE systems with a smoothing convex approximation
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DOI：
10.1051/cocv/2019077
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发表时间：
2020-09-30
影响因子：
1.4
通讯作者：
Li, Pu
中科院分区：
文献类型：
--
作者：
Geletu, Abebe;Hoffmann, Armin;Li, Pu
本文研究具有随机参数和约束状态变量的椭圆型偏微分方程系统的机会约束优化问题。我们证明了在标准假设下，CCPDE是一个凸优化问题。由于机会约束优化问题通常是非光滑的，难以直接求解，我们提出了一种光滑的内外近似方法来生成CCPDE的光滑近似问题序列。因此，凸CCPDE的最优解可以通过内外逼近问题的最优解逼近。数值算例验证了该方法的可行性。
In this paper, we consider chance constrained optimization of elliptic partial differential equation (CCPDE) systems with random parameters and constrained state variables. We demonstrate that, under standard assumptions, CCPDE is a convex optimization problem. Since chance constrained optimization problems are generally nonsmooth and difficult to solve directly, we propose a smoothing inner-outer approximation method to generate a sequence of smooth approximate problems for the CCPDE. Thus, the optimal solution of the convex CCPDE is approximable through optimal solutions of the inner-outer approximation problems. A numerical example demonstrates the viability of the proposed approach.