Lipschitz continuity of the gradient of a one-parametric class of SOC merit functions

Jein Shan Chen; Shaohua Pan

doi:10.1080/02331930802180319

Lipschitz continuity of the gradient of a one-parametric class of SOC merit functions

Jein Shan Chen, Shaohua Pan

Department of Mathematics

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

3 Citations (Scopus)

Abstract

In this article, we show that a one-parametric class of SOC merit functions has a Lipschitz continuous gradient; and moreover, the Lipschitz constant is related to the parameter in this class of SOC merit functions. This fact will lay a building block when the merit function approach as well as the Newton-type method are employed for solving the second-order cone complementarity problem with this class of merit functions.

Original language	English
Pages (from-to)	661-676
Number of pages	16
Journal	Optimization
Volume	59
Issue number	5
DOIs	https://doi.org/10.1080/02331930802180319
Publication status	Published - 2010 Jul

Keywords

Lipschitz continuity
Merit function
Second-order cone
Spectral factorization

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

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abstract = "In this article, we show that a one-parametric class of SOC merit functions has a Lipschitz continuous gradient; and moreover, the Lipschitz constant is related to the parameter in this class of SOC merit functions. This fact will lay a building block when the merit function approach as well as the Newton-type method are employed for solving the second-order cone complementarity problem with this class of merit functions.",

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

author = "Chen, {Jein Shan} and Shaohua Pan",

note = "Funding Information: 1. Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author{\textquoteright}s work is partially supported by National Science Council of Taiwan. E-mail: jschen@math.ntnu.edu.tw.",

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AU - Pan, Shaohua

N1 - Funding Information: 1. Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author’s work is partially supported by National Science Council of Taiwan. E-mail: jschen@math.ntnu.edu.tw.

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N2 - In this article, we show that a one-parametric class of SOC merit functions has a Lipschitz continuous gradient; and moreover, the Lipschitz constant is related to the parameter in this class of SOC merit functions. This fact will lay a building block when the merit function approach as well as the Newton-type method are employed for solving the second-order cone complementarity problem with this class of merit functions.

AB - In this article, we show that a one-parametric class of SOC merit functions has a Lipschitz continuous gradient; and moreover, the Lipschitz constant is related to the parameter in this class of SOC merit functions. This fact will lay a building block when the merit function approach as well as the Newton-type method are employed for solving the second-order cone complementarity problem with this class of merit functions.

KW - Lipschitz continuity

KW - Merit function

KW - Second-order cone

KW - Spectral factorization

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Lipschitz continuity of the gradient of a one-parametric class of SOC merit functions

Abstract

Keywords

ASJC Scopus subject areas

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