Second-order differentiability of probability functions
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- 作者：Wim van Ackooij ; Jérôme Malick
- 关键词：Stochastic optimization ; Probabilistic constraints ; Joint ; chance ; constraints ; Differentiability of probabilistic function ; Nonlinear optimization
- 刊名：Optimization Letters
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：11
- 期：1
- 页码：179-194
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Optimization; Operation Research/Decision Theory; Computational Intelligence; Numerical and Computational Physics, Simulation;
- 出版者：Springer Berlin Heidelberg
- ISSN：1862-4480
- 卷排序：11
文摘
In this paper, we study second-order differentiability properties of probability functions. We present conditions under which probability functions involving nonlinear systems and Gaussian (or Student) multi-variate random vectors are twice continuously differentiable. We provide an expression for their Hessian that can be useful in numerical methods for solving probabilistic constrained optimization problems.