Analytic approximation and differentiability of joint chance constraints
Analytic approximation and differentiability of joint chance constraints
复制标题
DOI：
10.1080/02331934.2019.1643344
复制
发表时间：
2019-07-25
期刊：
影响因子：
2.2
通讯作者：
Li, P.
中科院分区：
文献类型：
--
作者：
Geletu, A.;Hoffmann, A.;Li, P.
最近发展了一种求解单次机会约束优化（SCCOPT）问题的内外近似方法。在本文中，我们将这种方法扩展到解决联合机会约束优化（JCCOPT）问题。利用内-外逼近，定义了两个光滑参数优化问题，其可行集分别从内和外收敛到JCCOPT的可行集。内逼近问题的任何最优解对于JCCOPT都是先验可行的。当逼近参数趋于零时，内问题和外问题解的子序列分别渐进收敛于JCCOPT的最优解。作为主要结果，通过检验参数近似的梯度的一致收敛性，得到了联合机会约束的概率函数的连续可微性。
An inner-outer approximation approach was recently developed to solve single chance constrained optimization (SCCOPT) problems. In this paper, we extend this approach to address joint chance constrained optimization (JCCOPT) problems. Using an inner-outer approximation, two smooth parametric optimization problems are defined whose feasible sets converge to the feasible set of JCCOPT from inside and outside, respectively. Any optimal solution of the inner approximation problem is a priori feasible to the JCCOPT. As the approximation parameter tends to zero, a subsequence of the solutions of the inner and outer problems, respectively, converge asymptotically to an optimal solution of the JCCOPT. As a main result, the continuous differentiability of the probability function of a joint chance constraint is obtained by examining the uniform convergence of the gradients of the parametric approximations.