Further relationship between second-order cone and positive semidefinite matrix cone

Jinchuan Zhou; Jingyong Tang; Jein Shan Chen

doi:10.1080/02331934.2016.1220553

Further relationship between second-order cone and positive semidefinite matrix cone

Jinchuan Zhou, Jingyong Tang, Jein Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

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

1 Citation (Scopus)

Abstract

It is well known that second-order cone (SOC) programming can be regarded as a special case of positive semidefinite programming using the arrow matrix. This paper further studies the relationship between SOCs and positive semidefinite matrix cones. In particular, we explore the relationship to expressions regarding distance, projection, tangent cone, normal cone and the KKT system. Understanding these relationships will help us see the connection and difference between the SOC and its PSD reformulation more clearly.

Original language	English
Pages (from-to)	2115-2133
Number of pages	19
Journal	Optimization
Volume	65
Issue number	12
DOIs	https://doi.org/10.1080/02331934.2016.1220553
Publication status	Published - 2016 Dec 1

Keywords

KKT system
Positive semidefinite matrix cone
normal cone
projection
second-order cone
tangent cone

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

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10.1080/02331934.2016.1220553

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title = "Further relationship between second-order cone and positive semidefinite matrix cone",

abstract = "It is well known that second-order cone (SOC) programming can be regarded as a special case of positive semidefinite programming using the arrow matrix. This paper further studies the relationship between SOCs and positive semidefinite matrix cones. In particular, we explore the relationship to expressions regarding distance, projection, tangent cone, normal cone and the KKT system. Understanding these relationships will help us see the connection and difference between the SOC and its PSD reformulation more clearly.",

keywords = "KKT system, Positive semidefinite matrix cone, normal cone, projection, second-order cone, tangent cone",

author = "Jinchuan Zhou and Jingyong Tang and Chen, {Jein Shan}",

note = "Publisher Copyright: {\textcopyright} 2016 Informa UK Limited, trading as Taylor & Francis Group.",

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AU - Zhou, Jinchuan

AU - Tang, Jingyong

AU - Chen, Jein Shan

PY - 2016/12/1

Y1 - 2016/12/1

N2 - It is well known that second-order cone (SOC) programming can be regarded as a special case of positive semidefinite programming using the arrow matrix. This paper further studies the relationship between SOCs and positive semidefinite matrix cones. In particular, we explore the relationship to expressions regarding distance, projection, tangent cone, normal cone and the KKT system. Understanding these relationships will help us see the connection and difference between the SOC and its PSD reformulation more clearly.

AB - It is well known that second-order cone (SOC) programming can be regarded as a special case of positive semidefinite programming using the arrow matrix. This paper further studies the relationship between SOCs and positive semidefinite matrix cones. In particular, we explore the relationship to expressions regarding distance, projection, tangent cone, normal cone and the KKT system. Understanding these relationships will help us see the connection and difference between the SOC and its PSD reformulation more clearly.

KW - KKT system

KW - Positive semidefinite matrix cone

KW - normal cone

KW - projection

KW - second-order cone

KW - tangent cone

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EP - 2133

JO - Optimization

JF - Optimization

IS - 12

ER -

Further relationship between second-order cone and positive semidefinite matrix cone

Abstract

Keywords

ASJC Scopus subject areas

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