A second-order cone programming approach for linear programs with joint probabilistic constraints

Jianqiang Cheng; Abdel Lisser

doi:10.1016/j.orl.2012.06.008

A second-order cone programming approach for linear programs with joint probabilistic constraints

Jianqiang Cheng, Abdel Lisser

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

65 Scopus citations

Abstract

This paper deals with a special case of Linear Programs with joint Probabilistic Constraints (LPPC) with normally distributed coefficients and independent matrix vector rows. Through the piecewise linear approximation and the piecewise tangent approximation, we approximate the stochastic linear programs with two second-order cone programming (SOCP for short) problems. Furthermore, the optimal values of the two SOCP problems are a lower and upper bound of the original problem respectively. Finally, numerical experiments are given on randomly generated data.

Original language	English (US)
Pages (from-to)	325-328
Number of pages	4
Journal	Operations Research Letters
Volume	40
Issue number	5
DOIs	https://doi.org/10.1016/j.orl.2012.06.008
State	Published - Sep 2012
Externally published	Yes

Keywords

Joint probabilistic constraints
Piecewise linear approximation
Second-order cone 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.2012.06.008

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title = "A second-order cone programming approach for linear programs with joint probabilistic constraints",

abstract = "This paper deals with a special case of Linear Programs with joint Probabilistic Constraints (LPPC) with normally distributed coefficients and independent matrix vector rows. Through the piecewise linear approximation and the piecewise tangent approximation, we approximate the stochastic linear programs with two second-order cone programming (SOCP for short) problems. Furthermore, the optimal values of the two SOCP problems are a lower and upper bound of the original problem respectively. Finally, numerical experiments are given on randomly generated data.",

keywords = "Joint probabilistic constraints, Piecewise linear approximation, Second-order cone programming, Stochastic programming",

author = "Jianqiang Cheng and Abdel Lisser",

note = "Funding Information: The research of Jianqiang Cheng was supported by a China Scholarship Council (CSC) grant. ",

year = "2012",

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doi = "10.1016/j.orl.2012.06.008",

language = "English (US)",

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T1 - A second-order cone programming approach for linear programs with joint probabilistic constraints

AU - Cheng, Jianqiang

AU - Lisser, Abdel

N1 - Funding Information: The research of Jianqiang Cheng was supported by a China Scholarship Council (CSC) grant.

PY - 2012/9

Y1 - 2012/9

N2 - This paper deals with a special case of Linear Programs with joint Probabilistic Constraints (LPPC) with normally distributed coefficients and independent matrix vector rows. Through the piecewise linear approximation and the piecewise tangent approximation, we approximate the stochastic linear programs with two second-order cone programming (SOCP for short) problems. Furthermore, the optimal values of the two SOCP problems are a lower and upper bound of the original problem respectively. Finally, numerical experiments are given on randomly generated data.

AB - This paper deals with a special case of Linear Programs with joint Probabilistic Constraints (LPPC) with normally distributed coefficients and independent matrix vector rows. Through the piecewise linear approximation and the piecewise tangent approximation, we approximate the stochastic linear programs with two second-order cone programming (SOCP for short) problems. Furthermore, the optimal values of the two SOCP problems are a lower and upper bound of the original problem respectively. Finally, numerical experiments are given on randomly generated data.

KW - Joint probabilistic constraints

KW - Piecewise linear approximation

KW - Second-order cone programming

KW - Stochastic programming

UR - http://www.scopus.com/inward/record.url?scp=84864476267&partnerID=8YFLogxK

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VL - 40

SP - 325

EP - 328

JO - Operations Research Letters

JF - Operations Research Letters

IS - 5

ER -

A second-order cone programming approach for linear programs with joint probabilistic constraints

Abstract

Keywords

ASJC Scopus subject areas

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