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^*

^*Corresponding author for this work

Department of Mathematics

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

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	387-413
Number of pages	27
Journal	Numerical Functional Analysis and Optimization
Volume	31
Issue number	4
DOIs	https://doi.org/10.1080/01630563.2010.485334
Publication status	Published - 2010 Apr

Keywords

Error bound
Fixed point
Hilbert space
Level set
Merit functions
Second-order cone

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

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10.1080/01630563.2010.485334

Cite this

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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.",

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doi = "10.1080/01630563.2010.485334",

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pages = "387--413",

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TY - JOUR

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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DO - 10.1080/01630563.2010.485334

M3 - Article

AN - SCOPUS:77953515442

SN - 0163-0563

VL - 31

SP - 387

EP - 413

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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