Stationary point conditions for the FB merit function associated with symmetric cones

Shaohua Pan; Yu Lin Chang; Jein Shan Chen

doi:10.1016/j.orl.2010.07.011

Stationary point conditions for the FB merit function associated with symmetric cones

Shaohua Pan, Yu Lin Chang, Jein Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

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

7 Citations (Scopus)

Abstract

For the symmetric cone complementarity problem, we show that each stationary point of the unconstrained minimization reformulation based on the FischerBurmeister merit function is a solution to the problem, provided that the gradient operators of the mappings involved in the problem satisfy column monotonicity or have the Cartesian P0-property. These results answer the open question proposed in the article that appeared in Journal of Mathematical Analysis and Applications 355 (2009) 195215.

Original language	English
Pages (from-to)	372-377
Number of pages	6
Journal	Operations Research Letters
Volume	38
Issue number	5
DOIs	https://doi.org/10.1016/j.orl.2010.07.011
Publication status	Published - 2010 Sept

Keywords

FischerBurmeister merit function
Stationary points
Symmetric cones

ASJC Scopus subject areas

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

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10.1016/j.orl.2010.07.011

Cite this

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title = "Stationary point conditions for the FB merit function associated with symmetric cones",

abstract = "For the symmetric cone complementarity problem, we show that each stationary point of the unconstrained minimization reformulation based on the FischerBurmeister merit function is a solution to the problem, provided that the gradient operators of the mappings involved in the problem satisfy column monotonicity or have the Cartesian P0-property. These results answer the open question proposed in the article that appeared in Journal of Mathematical Analysis and Applications 355 (2009) 195215.",

keywords = "FischerBurmeister merit function, Stationary points, Symmetric cones",

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

note = "Funding Information: The authors thank the referees for their carefully reading of this paper and helpful suggestions. The first author{\textquoteright}s work is supported by National Young Natural Science Foundation (No. 10901058 ) and Guangdong Natural Science Foundation (No. 9251802902000001 ). The third author is a member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office and his work is supported by National Science Council of Taiwan . ",

year = "2010",

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doi = "10.1016/j.orl.2010.07.011",

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T1 - Stationary point conditions for the FB merit function associated with symmetric cones

AU - Pan, Shaohua

AU - Chang, Yu Lin

AU - Chen, Jein Shan

N1 - Funding Information: The authors thank the referees for their carefully reading of this paper and helpful suggestions. The first author’s work is supported by National Young Natural Science Foundation (No. 10901058 ) and Guangdong Natural Science Foundation (No. 9251802902000001 ). The third author is a member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office and his work is supported by National Science Council of Taiwan .

PY - 2010/9

Y1 - 2010/9

N2 - For the symmetric cone complementarity problem, we show that each stationary point of the unconstrained minimization reformulation based on the FischerBurmeister merit function is a solution to the problem, provided that the gradient operators of the mappings involved in the problem satisfy column monotonicity or have the Cartesian P0-property. These results answer the open question proposed in the article that appeared in Journal of Mathematical Analysis and Applications 355 (2009) 195215.

AB - For the symmetric cone complementarity problem, we show that each stationary point of the unconstrained minimization reformulation based on the FischerBurmeister merit function is a solution to the problem, provided that the gradient operators of the mappings involved in the problem satisfy column monotonicity or have the Cartesian P0-property. These results answer the open question proposed in the article that appeared in Journal of Mathematical Analysis and Applications 355 (2009) 195215.

KW - FischerBurmeister merit function

KW - Stationary points

KW - Symmetric cones

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EP - 377

JO - Operations Research Letters

JF - Operations Research Letters

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ER -

Stationary point conditions for the FB merit function associated with symmetric cones

Abstract

Keywords

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