Risk optimization with p-order conic constraints: A linear programming approach

Pavlo A. Krokhmal; Policarpio Soberanis

doi:10.1016/j.ejor.2009.03.053

Risk optimization with p-order conic constraints: A linear programming approach

Pavlo A. Krokhmal, Policarpio Soberanis

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

21 Scopus citations

Abstract

The paper considers solving of linear programming problems with p-order conic constraints that are related to a certain class of stochastic optimization models with risk objective or constraints. The proposed approach is based on construction of polyhedral approximations for p-order cones, and then invoking a Benders decomposition scheme that allows for efficient solving of the approximating problems. The conducted case study of portfolio optimization with p-order conic constraints demonstrates that the developed computational techniques compare favorably against a number of benchmark methods, including second-order conic programming methods.

Original language	English (US)
Pages (from-to)	653-671
Number of pages	19
Journal	European Journal of Operational Research
Volume	201
Issue number	3
DOIs	https://doi.org/10.1016/j.ejor.2009.03.053
State	Published - Mar 16 2010
Externally published	Yes

Keywords

Polyhedral approximation
Portfolio optimization
Risk measures
Second-order conic programming
Stochastic programming
p-order conic programming

ASJC Scopus subject areas

General Computer Science
Modeling and Simulation
Management Science and Operations Research
Information Systems and Management

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10.1016/j.ejor.2009.03.053

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title = "Risk optimization with p-order conic constraints: A linear programming approach",

abstract = "The paper considers solving of linear programming problems with p-order conic constraints that are related to a certain class of stochastic optimization models with risk objective or constraints. The proposed approach is based on construction of polyhedral approximations for p-order cones, and then invoking a Benders decomposition scheme that allows for efficient solving of the approximating problems. The conducted case study of portfolio optimization with p-order conic constraints demonstrates that the developed computational techniques compare favorably against a number of benchmark methods, including second-order conic programming methods.",

keywords = "Polyhedral approximation, Portfolio optimization, Risk measures, Second-order conic programming, Stochastic programming, p-order conic programming",

author = "Krokhmal, {Pavlo A.} and Policarpio Soberanis",

note = "Funding Information: Supported in part by NSF Grant DMI 0457473. ",

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T2 - A linear programming approach

AU - Krokhmal, Pavlo A.

AU - Soberanis, Policarpio

N1 - Funding Information: Supported in part by NSF Grant DMI 0457473.

PY - 2010/3/16

Y1 - 2010/3/16

N2 - The paper considers solving of linear programming problems with p-order conic constraints that are related to a certain class of stochastic optimization models with risk objective or constraints. The proposed approach is based on construction of polyhedral approximations for p-order cones, and then invoking a Benders decomposition scheme that allows for efficient solving of the approximating problems. The conducted case study of portfolio optimization with p-order conic constraints demonstrates that the developed computational techniques compare favorably against a number of benchmark methods, including second-order conic programming methods.

AB - The paper considers solving of linear programming problems with p-order conic constraints that are related to a certain class of stochastic optimization models with risk objective or constraints. The proposed approach is based on construction of polyhedral approximations for p-order cones, and then invoking a Benders decomposition scheme that allows for efficient solving of the approximating problems. The conducted case study of portfolio optimization with p-order conic constraints demonstrates that the developed computational techniques compare favorably against a number of benchmark methods, including second-order conic programming methods.

KW - Polyhedral approximation

KW - Portfolio optimization

KW - Risk measures

KW - Second-order conic programming

KW - Stochastic programming

KW - p-order conic programming

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JO - European Journal of Operational Research

JF - European Journal of Operational Research

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Risk optimization with p-order conic constraints: A linear programming approach

Abstract

Keywords

ASJC Scopus subject areas

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