A completely positive representation of 0-1 linear programs with joint probabilistic constraints

Jianqiang Cheng; Abdel Lisser

doi:10.1016/j.orl.2013.08.008

A completely positive representation of 0-1 linear programs with joint probabilistic constraints

Jianqiang Cheng, Abdel Lisser

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

4 Scopus citations

Abstract

In this paper, we study 0-1 linear programs with joint probabilistic constraints. The constraint matrix vector rows are assumed to be independent, and the coefficients to be normally distributed. Our main results show that this non-convex problem can be approximated by a convex completely positive problem. Moreover, we show that the optimal values of the latter converge to the optimal values of the original problem. Examples randomly generated highlight the efficiency of our approach.

Original language	English (US)
Pages (from-to)	597-601
Number of pages	5
Journal	Operations Research Letters
Volume	41
Issue number	6
DOIs	https://doi.org/10.1016/j.orl.2013.08.008
State	Published - 2013
Externally published	Yes

Keywords

0-1 linear program
Completely positive problems
Joint probabilistic constraints
Semidefinite programming
Stochastic programming

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2013.08.008

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title = "A completely positive representation of 0-1 linear programs with joint probabilistic constraints",

abstract = "In this paper, we study 0-1 linear programs with joint probabilistic constraints. The constraint matrix vector rows are assumed to be independent, and the coefficients to be normally distributed. Our main results show that this non-convex problem can be approximated by a convex completely positive problem. Moreover, we show that the optimal values of the latter converge to the optimal values of the original problem. Examples randomly generated highlight the efficiency of our approach.",

keywords = "0-1 linear program, Completely positive problems, Joint probabilistic constraints, Semidefinite programming, Stochastic programming",

author = "Jianqiang Cheng and Abdel Lisser",

note = "Funding Information: The research of Jianqiang Cheng and Abdel Lisser was supported by a China Scholarship Council (CSC) grant, and Hadamard Foundation , PGMO Program respectively. ",

year = "2013",

doi = "10.1016/j.orl.2013.08.008",

language = "English (US)",

volume = "41",

pages = "597--601",

journal = "Operations Research Letters",

issn = "0167-6377",

publisher = "Elsevier B.V.",

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T1 - A completely positive representation of 0-1 linear programs with joint probabilistic constraints

AU - Cheng, Jianqiang

AU - Lisser, Abdel

N1 - Funding Information: The research of Jianqiang Cheng and Abdel Lisser was supported by a China Scholarship Council (CSC) grant, and Hadamard Foundation , PGMO Program respectively.

PY - 2013

Y1 - 2013

N2 - In this paper, we study 0-1 linear programs with joint probabilistic constraints. The constraint matrix vector rows are assumed to be independent, and the coefficients to be normally distributed. Our main results show that this non-convex problem can be approximated by a convex completely positive problem. Moreover, we show that the optimal values of the latter converge to the optimal values of the original problem. Examples randomly generated highlight the efficiency of our approach.

AB - In this paper, we study 0-1 linear programs with joint probabilistic constraints. The constraint matrix vector rows are assumed to be independent, and the coefficients to be normally distributed. Our main results show that this non-convex problem can be approximated by a convex completely positive problem. Moreover, we show that the optimal values of the latter converge to the optimal values of the original problem. Examples randomly generated highlight the efficiency of our approach.

KW - 0-1 linear program

KW - Completely positive problems

KW - Joint probabilistic constraints

KW - Semidefinite programming

KW - Stochastic programming

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DO - 10.1016/j.orl.2013.08.008

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SN - 0167-6377

VL - 41

SP - 597

EP - 601

JO - Operations Research Letters

JF - Operations Research Letters

IS - 6

ER -

A completely positive representation of 0-1 linear programs with joint probabilistic constraints

Abstract

Keywords

ASJC Scopus subject areas

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