A globally convergent conjugate gradient method for minimizing self-concordant functions with application to constrained optimisation problems

Huibo Ji; Minyi Huang; John B. Moore; Jonathan H. Manton

doi:10.1109/ACC.2007.4282797

A globally convergent conjugate gradient method for minimizing self-concordant functions with application to constrained optimisation problems

Huibo Ji^*, Minyi Huang, John B. Moore, Jonathan H. Manton

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Self-concordant functions are a special class of convex functions introduced by Nesterov and Nemirovskii and used in interior point methods. This paper proposes a damped conjugate gradient method for optimization of self-concordant functions. This method is an ordinary conjugate gradient method but with a novel step-size selection rule which is proved to ensure the algorithm converges to the global minimum. As an example, the algorithm is applied to a quadratically constrained quadratic optimization problem.

Original language	English
Title of host publication	Proceedings of the 2007 American Control Conference, ACC
Pages	540-545
Number of pages	6
DOIs	https://doi.org/10.1109/ACC.2007.4282797
Publication status	Published - 2007
Event	2007 American Control Conference, ACC - New York, NY, United States Duration: 9 Jul 2007 → 13 Jul 2007

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Conference

Conference	2007 American Control Conference, ACC
Country/Territory	United States
City	New York, NY
Period	9/07/07 → 13/07/07

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10.1109/ACC.2007.4282797

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Ji, H., Huang, M., Moore, J. B., & Manton, J. H. (2007). A globally convergent conjugate gradient method for minimizing self-concordant functions with application to constrained optimisation problems. In Proceedings of the 2007 American Control Conference, ACC (pp. 540-545). Article 4282797 (Proceedings of the American Control Conference). https://doi.org/10.1109/ACC.2007.4282797

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title = "A globally convergent conjugate gradient method for minimizing self-concordant functions with application to constrained optimisation problems",

abstract = "Self-concordant functions are a special class of convex functions introduced by Nesterov and Nemirovskii and used in interior point methods. This paper proposes a damped conjugate gradient method for optimization of self-concordant functions. This method is an ordinary conjugate gradient method but with a novel step-size selection rule which is proved to ensure the algorithm converges to the global minimum. As an example, the algorithm is applied to a quadratically constrained quadratic optimization problem.",

author = "Huibo Ji and Minyi Huang and Moore, {John B.} and Manton, {Jonathan H.}",

year = "2007",

doi = "10.1109/ACC.2007.4282797",

language = "English",

isbn = "1424409888",

series = "Proceedings of the American Control Conference",

pages = "540--545",

booktitle = "Proceedings of the 2007 American Control Conference, ACC",

note = "2007 American Control Conference, ACC ; Conference date: 09-07-2007 Through 13-07-2007",

}

Ji, H, Huang, M, Moore, JB & Manton, JH 2007, A globally convergent conjugate gradient method for minimizing self-concordant functions with application to constrained optimisation problems. in Proceedings of the 2007 American Control Conference, ACC., 4282797, Proceedings of the American Control Conference, pp. 540-545, 2007 American Control Conference, ACC, New York, NY, United States, 9/07/07. https://doi.org/10.1109/ACC.2007.4282797

A globally convergent conjugate gradient method for minimizing self-concordant functions with application to constrained optimisation problems. / Ji, Huibo; Huang, Minyi; Moore, John B. et al.
Proceedings of the 2007 American Control Conference, ACC. 2007. p. 540-545 4282797 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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AU - Manton, Jonathan H.

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N2 - Self-concordant functions are a special class of convex functions introduced by Nesterov and Nemirovskii and used in interior point methods. This paper proposes a damped conjugate gradient method for optimization of self-concordant functions. This method is an ordinary conjugate gradient method but with a novel step-size selection rule which is proved to ensure the algorithm converges to the global minimum. As an example, the algorithm is applied to a quadratically constrained quadratic optimization problem.

AB - Self-concordant functions are a special class of convex functions introduced by Nesterov and Nemirovskii and used in interior point methods. This paper proposes a damped conjugate gradient method for optimization of self-concordant functions. This method is an ordinary conjugate gradient method but with a novel step-size selection rule which is proved to ensure the algorithm converges to the global minimum. As an example, the algorithm is applied to a quadratically constrained quadratic optimization problem.

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M3 - Conference contribution

SN - 1424409888

SN - 9781424409884

T3 - Proceedings of the American Control Conference

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BT - Proceedings of the 2007 American Control Conference, ACC

T2 - 2007 American Control Conference, ACC

Y2 - 9 July 2007 through 13 July 2007

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A globally convergent conjugate gradient method for minimizing self-concordant functions with application to constrained optimisation problems

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