Using schur complement theorem to prove convexity of some SOC-functions

Jein Shan Chen; Tsun Ko Liao; Shaohua Pan

Using schur complement theorem to prove convexity of some SOC-functions

Jein Shan Chen, Tsun Ko Liao, Shaohua Pan

Department of Mathematics

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

7 Citations (Scopus)

Abstract

In this paper, we provide an important application of the Schur Complement Theorem in establishing convexity of some functions associated with second-order cones (SOCs), called SOC-trace functions. As illustrated in the paper, these functions play a key role in the development of penalty and barrier functions methods for second-order cone programs, and establishment of some important inequalities associated with SOCs.

Original language	English
Pages (from-to)	421-431
Number of pages	11
Journal	Journal of Nonlinear and Convex Analysis
Volume	13
Issue number	3
Publication status	Published - 2012 Jul

Keywords

Convexity
Positive semidefiniteness
SOC-functions
Second-order cone

ASJC Scopus subject areas

Analysis
Geometry and Topology
Control and Optimization
Applied Mathematics

Cite this

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KW - Positive semidefiniteness

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KW - Second-order cone

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Using schur complement theorem to prove convexity of some SOC-functions

Abstract

Keywords

ASJC Scopus subject areas

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