Second-order differentiability of probability functions

被引：15

作者：

van Ackooij, Wim ^{[1
]}

Malick, Jerome ^{[2
]}

机构：

[1] EDF R&D, OSIRIS, 1 Ave Gen Gaulle, F-92141 Clamart, France

[2] CNRS, LJK, F-38000 Grenoble, France

来源：

OPTIMIZATION LETTERS | 2017年 / 11卷 / 01期

关键词：

Stochastic optimization; Probabilistic constraints; Joint-chanceconstraints; Differentiability of probabilistic function; Nonlinear optimization; CHANCE CONSTRAINTS; BUNDLE METHODS; OPTIMIZATION; CONVEXITY;

D O I：

10.1007/s11590-016-1015-7

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：179 / 194

页数：16

共 25 条

[1]

[Anonymous], 2009, Computation of Multivariate Normal and t Probabilities

[2]

[Anonymous], 2001, Applied Analysis

[3]

Arnold T, 2014, PAC J OPTIM, V10, P5

[4] Probabilistic constraints via SQP solver: application to a renewable energy management problem [J].

Bremer I. ;

Henrion R. ;

Möller A. .

Computational Management Science, 2015, 12 (3) :435-459

[5] Subroutines for computing normal probabilities of sets -: Computer experiences [J].

Deák, I .

ANNALS OF OPERATIONS RESEARCH, 2000, 100 (1-4) :103-122

[6]

Deak I., 1986, Journal of Statistical Computation and Simulation, P101, DOI 10.1080/00949658608810951

[7] Optimization of a continuous distillation process under random inflow rate [J].

Henrion, R ;

Möller, A .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2003, 45 (1-3) :247-262

[8]

Henrion R, 2011, Stochastic optimization methods in finance and Energy, P427

[9] Convexity of chance constraints with independent random variables [J].

Henrion, Rene ;

Strugarek, Cyrille .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2008, 41 (02) :263-276

[10] A Gradient Formula for Linear Chance Constraints Under Gaussian Distribution [J].

Henrion, Rene ;

Moeller, Andris .

MATHEMATICS OF OPERATIONS RESEARCH, 2012, 37 (03) :475-488

← 1 2 3 →