Chance constrained 0–1 quadratic programs using copulas

Jianqiang Cheng; Michal Houda; Abdel Lisser

doi:10.1007/s11590-015-0854-y

Chance constrained 0–1 quadratic programs using copulas

Jianqiang Cheng, Michal Houda, Abdel Lisser

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

In this paper, we study 0–1 quadratic programs with joint probabilistic constraints. The row vectors of the constraint matrix are assumed to be normally distributed but are not supposed to be independent. We propose a mixed integer linear reformulation and provide an efficient semidefinite relaxation of the original problem. The dependence of the random vectors is handled by the means of copulas. Finally, numerical experiments are conducted to show the strength of our approach.

Original language	English (US)
Pages (from-to)	1283-1295
Number of pages	13
Journal	Optimization Letters
Volume	9
Issue number	7
DOIs	https://doi.org/10.1007/s11590-015-0854-y
State	Published - Oct 22 2015
Externally published	Yes

Keywords

0–1 quadratic program
Copula theory
Joint probabilistic constraints
Semidefinite programming
Stochastic programming

ASJC Scopus subject areas

Control and Optimization

Access to Document

10.1007/s11590-015-0854-y

Cite this

@article{ebbe6191ba214eec8709b069310b0c8e,

title = "Chance constrained 0–1 quadratic programs using copulas",

abstract = "In this paper, we study 0–1 quadratic programs with joint probabilistic constraints. The row vectors of the constraint matrix are assumed to be normally distributed but are not supposed to be independent. We propose a mixed integer linear reformulation and provide an efficient semidefinite relaxation of the original problem. The dependence of the random vectors is handled by the means of copulas. Finally, numerical experiments are conducted to show the strength of our approach.",

keywords = "0–1 quadratic program, Copula theory, Joint probabilistic constraints, Semidefinite programming, Stochastic programming",

author = "Jianqiang Cheng and Michal Houda and Abdel Lisser",

note = "Funding Information: This research was supported by Fondation Math{\'e}matiques Jacques Hadamard, PGMO/IROE grant No. 2012-042H. Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",

year = "2015",

month = oct,

day = "22",

doi = "10.1007/s11590-015-0854-y",

language = "English (US)",

volume = "9",

pages = "1283--1295",

journal = "Optimization Letters",

issn = "1862-4472",

publisher = "Springer Verlag",

number = "7",

}

TY - JOUR

T1 - Chance constrained 0–1 quadratic programs using copulas

AU - Cheng, Jianqiang

AU - Houda, Michal

AU - Lisser, Abdel

PY - 2015/10/22

Y1 - 2015/10/22

N2 - In this paper, we study 0–1 quadratic programs with joint probabilistic constraints. The row vectors of the constraint matrix are assumed to be normally distributed but are not supposed to be independent. We propose a mixed integer linear reformulation and provide an efficient semidefinite relaxation of the original problem. The dependence of the random vectors is handled by the means of copulas. Finally, numerical experiments are conducted to show the strength of our approach.

AB - In this paper, we study 0–1 quadratic programs with joint probabilistic constraints. The row vectors of the constraint matrix are assumed to be normally distributed but are not supposed to be independent. We propose a mixed integer linear reformulation and provide an efficient semidefinite relaxation of the original problem. The dependence of the random vectors is handled by the means of copulas. Finally, numerical experiments are conducted to show the strength of our approach.

KW - 0–1 quadratic program

KW - Copula theory

KW - Joint probabilistic constraints

KW - Semidefinite programming

KW - Stochastic programming

UR - http://www.scopus.com/inward/record.url?scp=84941939714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941939714&partnerID=8YFLogxK

U2 - 10.1007/s11590-015-0854-y

DO - 10.1007/s11590-015-0854-y

M3 - Article

AN - SCOPUS:84941939714

SN - 1862-4472

VL - 9

SP - 1283

EP - 1295

JO - Optimization Letters

JF - Optimization Letters

IS - 7

ER -

Chance constrained 0–1 quadratic programs using copulas

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this