Analyticity of weighted central paths and error bounds for semidefinite programming
The purpose of this paper is two-fold. Firstly, we show that every Cholesky-based weighted central path for semi definite programming is analytic under strict complementarity. This result is applied to homogeneous cone programming to show that the central paths defined by the known class of optimal...
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sg-ntu-dr.10356-913562023-02-28T19:36:59Z Analyticity of weighted central paths and error bounds for semidefinite programming Chua, Chek Beng. School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Applied mathematics::Optimization The purpose of this paper is two-fold. Firstly, we show that every Cholesky-based weighted central path for semi definite programming is analytic under strict complementarity. This result is applied to homogeneous cone programming to show that the central paths defined by the known class of optimal self-concordant barriers are analytic in the presence of strictly complementary solutions. Secondly, we consider a sequence of primal-dual solutions that lies within a prescribed neighborhood of the central path of a pair of primal-dual semi definite programming problems, and converges to the respective optimal faces. Under the additional assumption of strict complementarity, we derive two necessary and sufficient conditions for the sequence of primal-dual solutions to converge linearly with their duality gaps. Accepted version 2009-07-29T09:08:18Z 2019-12-06T18:04:12Z 2009-07-29T09:08:18Z 2019-12-06T18:04:12Z 2007 2007 Journal Article Chua, C. B. (2007). Analyticity of weighted central paths and error bounds for semidefinite programming. Mathematical Programming, 239-271. 0025-5610 https://hdl.handle.net/10356/91356 http://hdl.handle.net/10220/5855 10.1007/s10107-007-0155-z en Mathematical programming Mathematical Programming @ copyright 2007 Springer-Verlag. The journal's website is located at http://www.springerlink.com.ezlibproxy1.ntu.edu.sg/content/103081. 28 p. application/pdf |
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DRNTU::Science::Mathematics::Applied mathematics::Optimization Chua, Chek Beng. Analyticity of weighted central paths and error bounds for semidefinite programming |
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The purpose of this paper is two-fold. Firstly, we show that every Cholesky-based weighted central path for semi definite programming is analytic under strict complementarity. This result is applied to homogeneous cone programming to show that the central paths defined by the known class of optimal self-concordant barriers are analytic in the presence of strictly complementary solutions. Secondly, we consider a sequence of primal-dual solutions that lies within a prescribed neighborhood of the central path of a pair of primal-dual semi definite programming problems, and converges to the respective optimal faces. Under the additional assumption of strict complementarity, we derive two necessary and sufficient conditions for the sequence of primal-dual solutions to converge linearly with their duality gaps. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Chua, Chek Beng. |
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Article |
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Chua, Chek Beng. |
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Chua, Chek Beng. |
title |
Analyticity of weighted central paths and error bounds for semidefinite programming |
title_short |
Analyticity of weighted central paths and error bounds for semidefinite programming |
title_full |
Analyticity of weighted central paths and error bounds for semidefinite programming |
title_fullStr |
Analyticity of weighted central paths and error bounds for semidefinite programming |
title_full_unstemmed |
Analyticity of weighted central paths and error bounds for semidefinite programming |
title_sort |
analyticity of weighted central paths and error bounds for semidefinite programming |
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2009 |
url |
https://hdl.handle.net/10356/91356 http://hdl.handle.net/10220/5855 |
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1759854971129430016 |