A MCMC/Bernstein approach to chance constrained programs

Author

Zinan Zhao ; Kumar, Manoj

Author_Institution

Dept. of Mech. & Aerosp. Eng., Univ. of Florida, Gainesville, FL, USA

fYear

2014

fDate

4-6 June 2014

Firstpage

4318

Lastpage

4323

Abstract

This paper presents an extension of convex Bernstein approximations to non-affine and dependent chance constrained optimization problems. The Bernstein approximation technique transcribes probabilistic constraints into conservative convex deterministic constraints, relying heavily upon the evaluation of exponential moment generating functions. This is a computationally burdensome task for non-affine probabilistic constraints involving dependent random variables. In this paper, the theoretical framework of Bernstein approximations is combined with the practical benefits of Markov chain Monte Carlo (MCMC) integration for its use in a range of high dimensional applications. Numerical results for the combined Bernstein/MCMC approach are compared with scenario approximations.

Keywords

Markov processes; Monte Carlo methods; approximation theory; convex programming; Bernstein approximation technique; MCMC-Bernstein approach; Markov chain Monte Carlo approach; chance constrained optimization problems; convex Bernstein approximations; convex deterministic constraints; exponential moment generating functions; probabilistic constraints; random variables; scenario approximations; Approximation methods; Monte Carlo methods; Optimization; Portfolios; Probabilistic logic; Random variables; Vectors; Optimization; Optimization algorithms; Randomized algorithms;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference (ACC), 2014

Conference_Location

Portland, OR

ISSN

0743-1619

Print_ISBN

978-1-4799-3272-6

Type

conf

DOI

10.1109/ACC.2014.6859159

Filename

6859159