A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming

A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming

When using interior methods for solving semidefinite programming (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, based on a semismooth equation reformulation using Fisch...

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Main Authors: Aiqun Huang, Chengxian Xu
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2012/819607
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spelling doaj-bf6a3c947fb14cf483b47a0cf7e7ca292020-11-24T23:13:28ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472012-01-01201210.1155/2012/819607819607A Globally Convergent Filter-Type Trust Region Method for Semidefinite ProgrammingAiqun Huang0Chengxian Xu1School of Mathematics and Statistics, Xi'an Jiaotong University, Shaanxi, Xi'an 710049, ChinaSchool of Mathematics and Statistics, Xi'an Jiaotong University, Shaanxi, Xi'an 710049, ChinaWhen using interior methods for solving semidefinite programming (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, based on a semismooth equation reformulation using Fischer's function, we propose a filter method with trust region for solving large-scale SDP problems. At each iteration we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations. Under mild assumptions, the convergence of this algorithm is established. Numerical examples are given to illustrate the convergence results obtained.http://dx.doi.org/10.1155/2012/819607
collection DOAJ
language English
format Article
sources DOAJ
author Aiqun Huang
Chengxian Xu
spellingShingle Aiqun Huang
Chengxian Xu
A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming
Mathematical Problems in Engineering
author_facet Aiqun Huang
Chengxian Xu
author_sort Aiqun Huang
title A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming
title_short A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming
title_full A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming
title_fullStr A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming
title_full_unstemmed A Globally Convergent Filter-Type Trust Region Method for Semidefinite Programming
title_sort globally convergent filter-type trust region method for semidefinite programming
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2012-01-01
description When using interior methods for solving semidefinite programming (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, based on a semismooth equation reformulation using Fischer's function, we propose a filter method with trust region for solving large-scale SDP problems. At each iteration we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations. Under mild assumptions, the convergence of this algorithm is established. Numerical examples are given to illustrate the convergence results obtained.
url http://dx.doi.org/10.1155/2012/819607
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AT chengxianxu agloballyconvergentfiltertypetrustregionmethodforsemidefiniteprogramming
AT aiqunhuang globallyconvergentfiltertypetrustregionmethodforsemidefiniteprogramming
AT chengxianxu globallyconvergentfiltertypetrustregionmethodforsemidefiniteprogramming
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