On Second-Order Cone Functions

Shafu Jibrin; James W. Swift

doi:10.1155/2024/7090058

On Second-Order Cone Functions

Shafu Jibrin
, James W. Swift

Mathematics and Statistics

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

Abstract

We consider the second-order cone function (SOCF) (formula presented) defned by (formula presented), with parameters (formula presented).Every SOCF is concave.We give necessary and sufcient conditions for strict concavity of f. Te parameters A and b are not uniquely determined. We show that every SOCF can be written in the form (formula presented). We give necessary and sufcient conditions for the parameters c, d, δ, M = A^TA, and x_* to be uniquely determined. We also give necessary and sufcient conditions for f to be bounded above.

Original language	English (US)
Article number	7090058
Journal	Journal of Optimization
Volume	2024
DOIs	https://doi.org/10.1155/2024/7090058
State	Published - 2024

ASJC Scopus subject areas

Analysis
Control and Optimization
Decision Sciences (miscellaneous)

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10.1155/2024/7090058

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abstract = "We consider the second-order cone function (SOCF) (formula presented) defned by (formula presented), with parameters (formula presented).Every SOCF is concave.We give necessary and sufcient conditions for strict concavity of f. Te parameters A and b are not uniquely determined. We show that every SOCF can be written in the form (formula presented). We give necessary and sufcient conditions for the parameters c, d, δ, M = ATA, and x* to be uniquely determined. We also give necessary and sufcient conditions for f to be bounded above.",

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AB - We consider the second-order cone function (SOCF) (formula presented) defned by (formula presented), with parameters (formula presented).Every SOCF is concave.We give necessary and sufcient conditions for strict concavity of f. Te parameters A and b are not uniquely determined. We show that every SOCF can be written in the form (formula presented). We give necessary and sufcient conditions for the parameters c, d, δ, M = ATA, and x* to be uniquely determined. We also give necessary and sufcient conditions for f to be bounded above.

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On Second-Order Cone Functions

Abstract

ASJC Scopus subject areas

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