Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications

被引：0
作者：
B. K. Pagnoncelli
S. Ahmed
A. Shapiro
机构：
[1] Pontifícia Universidade Católica do Rio de Janeiro,Departamento de Matemática
[2] Georgia Institute of Technology,undefined
来源：
Journal of Optimization Theory and Applications | 2009年 / 142卷
关键词：
Chance constraints; Sample average approximation; Portfolio selection;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study sample approximations of chance constrained problems. In particular, we consider the sample average approximation (SAA) approach and discuss the convergence properties of the resulting problem. We discuss how one can use the SAA method to obtain good candidate solutions for chance constrained problems. Numerical experiments are performed to correctly tune the parameters involved in the SAA. In addition, we present a method for constructing statistical lower bounds for the optimal value of the considered problem and discuss how one should tune the underlying parameters. We apply the SAA to two chance constrained problems. The first is a linear portfolio selection problem with returns following a multivariate lognormal distribution. The second is a joint chance constrained version of a simple blending problem.
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页码：399 / 416
页数：17
相关论文
共 30 条
[1]  
Charnes A.(1958)Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil Manag. Sci. 4 235-263
[2]  
Cooper W.W.(1991)Stochastic programming in water management: a case study and a comparison of solution techniques Eur. J. Oper. Res. 52 28-44
[3]  
Symmonds G.H.(2003)Optimization of a continuous distillation process under random inflow rate Comput. Math. Appl. 45 247-262
[4]  
Dupačová J.(2000)Concavity and efficient points of discrete distributions in probabilistic programming Math. Program. 89 55-77
[5]  
Gaivoronski A.(2008)A sample approximation approach for optimization with probabilistic constraints SIAM J. Optim. 19 674-699
[6]  
Kos Z.(2006)Convex approximations of chance constrained programs SIAM J. Optim. 17 969-996
[7]  
Szántai T.(2008)Optimizing call center staffing using simulation and analytic center cutting plane methods Manag. Sci. 54 295-309
[8]  
Henrion R.(2008)A sample approximation approach for optimization with probabilistic constraints SIAM J. Optim. 19 674-699
[9]  
Möller A.(1996)Consistency of minimizers and the SLLN for stochastic programs J. Convex Anal. 2 1-17
[10]  
Dentcheva D.(1952)A measure of asymptotic efficiency for tests of a hypothesis based on the sum observations Ann. Math. Stat. 23 493-507
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