An interior point method for growing connected resistive networks

Sepideh Hassan Moghaddam; Mihailo R. Jovanovic

doi:10.1109/ACC.2015.7170900

An interior point method for growing connected resistive networks

Sepideh Hassan Moghaddam, Mihailo R. Jovanovic

Electrical and Computer Engineering

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

13 Scopus citations

Abstract

We consider the problem of growing connected networks of resistors where effective resistance is used as a performance metric. This problem can be cast as a semidefinite program by introducing an ℓ_l regularization into the optimal control formulation. For small networks this problem can be solved via standard interior point method solvers (e.g., SeDuMi or SDPT3). In this paper, we develop a primal-dual interior point algorithm that is well-suited for large-scale problems. The search direction is obtained using the direct method based on Cholesky factorization and iterative method based on the preconditioned conjugate gradient. We illustrate that both of these significantly outperform general-purpose solvers.

Original language	English (US)
Title of host publication	ACC 2015 - 2015 American Control Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1223-1228
Number of pages	6
ISBN (Electronic)	9781479986842
DOIs	https://doi.org/10.1109/ACC.2015.7170900
State	Published - Jul 28 2015
Event	2015 American Control Conference, ACC 2015 - Chicago, United States Duration: Jul 1 2015 → Jul 3 2015

Publication series

Name	Proceedings of the American Control Conference
Volume	2015-July
ISSN (Print)	0743-1619

Conference

Conference	2015 American Control Conference, ACC 2015
Country/Territory	United States
City	Chicago
Period	7/1/15 → 7/3/15

Bibliographical note

Publisher Copyright:
© 2015 American Automatic Control Council.

Keywords

Convex optimization
interior-point method
resistive networks
semidefinite programming
ℓ minimization

Publisher link

10.1109/ACC.2015.7170900

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An interior point method for growing connected resistive networks. / Hassan Moghaddam, Sepideh; Jovanovic, Mihailo R.
ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1223-1228 7170900 (Proceedings of the American Control Conference; Vol. 2015-July).

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

Hassan Moghaddam, S & Jovanovic, MR 2015, An interior point method for growing connected resistive networks. in ACC 2015 - 2015 American Control Conference., 7170900, Proceedings of the American Control Conference, vol. 2015-July, Institute of Electrical and Electronics Engineers Inc., pp. 1223-1228, 2015 American Control Conference, ACC 2015, Chicago, United States, 7/1/15. https://doi.org/10.1109/ACC.2015.7170900

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title = "An interior point method for growing connected resistive networks",

abstract = "We consider the problem of growing connected networks of resistors where effective resistance is used as a performance metric. This problem can be cast as a semidefinite program by introducing an ℓl regularization into the optimal control formulation. For small networks this problem can be solved via standard interior point method solvers (e.g., SeDuMi or SDPT3). In this paper, we develop a primal-dual interior point algorithm that is well-suited for large-scale problems. The search direction is obtained using the direct method based on Cholesky factorization and iterative method based on the preconditioned conjugate gradient. We illustrate that both of these significantly outperform general-purpose solvers.",

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N2 - We consider the problem of growing connected networks of resistors where effective resistance is used as a performance metric. This problem can be cast as a semidefinite program by introducing an ℓl regularization into the optimal control formulation. For small networks this problem can be solved via standard interior point method solvers (e.g., SeDuMi or SDPT3). In this paper, we develop a primal-dual interior point algorithm that is well-suited for large-scale problems. The search direction is obtained using the direct method based on Cholesky factorization and iterative method based on the preconditioned conjugate gradient. We illustrate that both of these significantly outperform general-purpose solvers.

AB - We consider the problem of growing connected networks of resistors where effective resistance is used as a performance metric. This problem can be cast as a semidefinite program by introducing an ℓl regularization into the optimal control formulation. For small networks this problem can be solved via standard interior point method solvers (e.g., SeDuMi or SDPT3). In this paper, we develop a primal-dual interior point algorithm that is well-suited for large-scale problems. The search direction is obtained using the direct method based on Cholesky factorization and iterative method based on the preconditioned conjugate gradient. We illustrate that both of these significantly outperform general-purpose solvers.

KW - Convex optimization

KW - interior-point method

KW - resistive networks

KW - semidefinite programming

KW - ℓ minimization

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An interior point method for growing connected resistive networks

Abstract

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Keywords

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