论文标题
用于偶然受限的非线性程序的Sigmoidal近似
A Sigmoidal Approximation for Chance-Constrained Nonlinear Programs
论文作者
论文摘要
我们为价值风险（称为Sigvar）提出了一个sigmoidal近似，并使用此近似来解决具有机会约束的非线性程序（NLP）。我们证明近似值是保守的，并且可以任意将保守主义水平限制为限制参数值。 SIGVAR近似具有比精确混合构成重新印度的可伸缩性优势，因为其样品平均近似可以作为标准NLP施加。我们还建立了文献中最近报道的Sigvar和其他光滑的Sigmoidal近似之间的明确连接。我们表明，Sigvar对这种近似值的关键优势是，可以与处于风险的条件值（CVAR）近似值建立明确的连接，并利用此连接以获得近似参数的初始猜测。我们提出了小规模和大规模的数值研究，以说明这些发展。
We propose a sigmoidal approximation for the value-at-risk (that we call SigVaR) and we use this approximation to tackle nonlinear programs (NLPs) with chance constraints. We prove that the approximation is conservative and that the level of conservatism can be made arbitrarily small for limiting parameter values. The SigVar approximation brings scalability benefits over exact mixed-integer reformulations because its sample average approximation can be cast as a standard NLP. We also establish explicit connections between SigVaR and other smooth sigmoidal approximations recently reported in the literature. We show that a key benefit of SigVaR over such approximations is that one can establish an explicit connection with the conditional value at risk (CVaR) approximation and exploit this connection to obtain initial guesses for the approximation parameters. We present small- and large-scale numerical studies to illustrate the developments.
