The SC1 property of the squared norm of the SOC Fischer-Burmeister function

Jein Shan Chen; Defeng Sun; Jie Sun

doi:10.1016/j.orl.2007.08.005

The SC¹ property of the squared norm of the SOC Fischer-Burmeister function

Jein Shan Chen^*, Defeng Sun, Jie Sun

^*Corresponding author for this work

Department of Mathematics

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

22 Citations (Scopus)

Abstract

We show that the gradient mapping of the squared norm of Fischer-Burmeister function is globally Lipschitz continuous and semismooth, which provides a theoretical basis for solving nonlinear second-order cone complementarity problems via the conjugate gradient method and the semismooth Newton's method.

Original language	English
Pages (from-to)	385-392
Number of pages	8
Journal	Operations Research Letters
Volume	36
Issue number	3
DOIs	https://doi.org/10.1016/j.orl.2007.08.005
Publication status	Published - 2008 May

Keywords

Lipschitz continuity
Merit function
Second-order cone
Semismoothness
Spectral factorization

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

Access to Document

10.1016/j.orl.2007.08.005

Cite this

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title = "The SC1 property of the squared norm of the SOC Fischer-Burmeister function",

abstract = "We show that the gradient mapping of the squared norm of Fischer-Burmeister function is globally Lipschitz continuous and semismooth, which provides a theoretical basis for solving nonlinear second-order cone complementarity problems via the conjugate gradient method and the semismooth Newton's method.",

keywords = "Lipschitz continuity, Merit function, Second-order cone, Semismoothness, Spectral factorization",

author = "Chen, {Jein Shan} and Defeng Sun and Jie Sun",

note = "Funding Information: Jein-Shan Chen is a member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office and his research is partially supported by the National Science Council of Taiwan. The research of Defeng Sun is partially supported by the Academic Research Fund under Grant No. R-146-000-104-112 of the National University of Singapore. The research of Jie Sun is partially supported by Singapore-MIT Alliance.",

year = "2008",

month = may,

doi = "10.1016/j.orl.2007.08.005",

language = "English",

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journal = "Operations Research Letters",

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AU - Chen, Jein Shan

AU - Sun, Defeng

AU - Sun, Jie

N1 - Funding Information: Jein-Shan Chen is a member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office and his research is partially supported by the National Science Council of Taiwan. The research of Defeng Sun is partially supported by the Academic Research Fund under Grant No. R-146-000-104-112 of the National University of Singapore. The research of Jie Sun is partially supported by Singapore-MIT Alliance.

PY - 2008/5

Y1 - 2008/5

N2 - We show that the gradient mapping of the squared norm of Fischer-Burmeister function is globally Lipschitz continuous and semismooth, which provides a theoretical basis for solving nonlinear second-order cone complementarity problems via the conjugate gradient method and the semismooth Newton's method.

AB - We show that the gradient mapping of the squared norm of Fischer-Burmeister function is globally Lipschitz continuous and semismooth, which provides a theoretical basis for solving nonlinear second-order cone complementarity problems via the conjugate gradient method and the semismooth Newton's method.

KW - Lipschitz continuity

KW - Merit function

KW - Second-order cone

KW - Semismoothness

KW - Spectral factorization

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