Two classes of merit functions for infinite-dimensional second order complimentary problems

Juhe Sun; Jein Shan Chen

doi:10.1080/01630563.2010.485334

Two classes of merit functions for infinite-dimensional second order complimentary problems

Juhe Sun, Jein Shan Chen^*

^*此作品的通信作者

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

2 引文斯高帕斯（Scopus）

摘要

In this article, we extend two classes of merit functions for the second-order complementarity problem (SOCP) to infinite-dimensional SOCP. These two classes of merit functions include several popular merit functions, which are used in nonlinear complementarity problem, (NCP)/(SDCP) semidefinite complementarity problem, and SOCP, as special cases. We give conditions under which the infinite-dimensional SOCP has a unique solution and show that all these merit functions provide an error bound for infinite-dimensional SOCP and have bounded level sets. These results are very useful for designing solution methods for infinite-dimensional SOCP.

原文	英語
頁（從 - 到）	387-413
頁數	27
期刊	Numerical Functional Analysis and Optimization
卷	31
發行號	4
DOIs	https://doi.org/10.1080/01630563.2010.485334
出版狀態	已發佈 - 2010 4月

ASJC Scopus subject areas

分析
訊號處理
電腦科學應用
控制和優化

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10.1080/01630563.2010.485334

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title = "Two classes of merit functions for infinite-dimensional second order complimentary problems",

abstract = "In this article, we extend two classes of merit functions for the second-order complementarity problem (SOCP) to infinite-dimensional SOCP. These two classes of merit functions include several popular merit functions, which are used in nonlinear complementarity problem, (NCP)/(SDCP) semidefinite complementarity problem, and SOCP, as special cases. We give conditions under which the infinite-dimensional SOCP has a unique solution and show that all these merit functions provide an error bound for infinite-dimensional SOCP and have bounded level sets. These results are very useful for designing solution methods for infinite-dimensional SOCP.",

keywords = "Error bound, Fixed point, Hilbert space, Level set, Merit functions, Second-order cone",

author = "Juhe Sun and Chen, {Jein Shan}",

note = "Funding Information: J.-S. Chen is a Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author{\textquoteright}s work is supported by National Science Council of Taiwan.",

year = "2010",

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doi = "10.1080/01630563.2010.485334",

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T1 - Two classes of merit functions for infinite-dimensional second order complimentary problems

AU - Sun, Juhe

AU - Chen, Jein Shan

N1 - Funding Information: J.-S. Chen is a Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author’s work is supported by National Science Council of Taiwan.

PY - 2010/4

Y1 - 2010/4

N2 - In this article, we extend two classes of merit functions for the second-order complementarity problem (SOCP) to infinite-dimensional SOCP. These two classes of merit functions include several popular merit functions, which are used in nonlinear complementarity problem, (NCP)/(SDCP) semidefinite complementarity problem, and SOCP, as special cases. We give conditions under which the infinite-dimensional SOCP has a unique solution and show that all these merit functions provide an error bound for infinite-dimensional SOCP and have bounded level sets. These results are very useful for designing solution methods for infinite-dimensional SOCP.

AB - In this article, we extend two classes of merit functions for the second-order complementarity problem (SOCP) to infinite-dimensional SOCP. These two classes of merit functions include several popular merit functions, which are used in nonlinear complementarity problem, (NCP)/(SDCP) semidefinite complementarity problem, and SOCP, as special cases. We give conditions under which the infinite-dimensional SOCP has a unique solution and show that all these merit functions provide an error bound for infinite-dimensional SOCP and have bounded level sets. These results are very useful for designing solution methods for infinite-dimensional SOCP.

KW - Error bound

KW - Fixed point

KW - Hilbert space

KW - Level set

KW - Merit functions

KW - Second-order cone

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ER -

Two classes of merit functions for infinite-dimensional second order complimentary problems

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