An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints

Armin Ataei; Qian Wang

doi:10.1109/acc.2012.6315611

An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints

Armin Ataei
, Qian Wang

Mechanical Engineering

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

4 Scopus citations

Abstract

In this paper, an efficient algorithm based on the ellipsoid method is proposed to solve a linear optimization problem over a set of uncertain Linear Matrix Inequalities (LMIs). First, an Ellipsoid Algorithm (EA) with deep cuts is introduced for solving the set of uncertain LMIs. The proposed ellipsoid algorithm is shown to converge to a probabilistically feasible point with high confidence level and in fewer iterations compared to other EA methods. Then, through a set of new cuts, the objective function is minimized while maintaining the probabilistic feasibility of the solution.

Original language	English (US)
Title of host publication	2012 American Control Conference, ACC 2012
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	857-862
Number of pages	6
ISBN (Print)	9781457710957
DOIs	https://doi.org/10.1109/acc.2012.6315611
State	Published - 2012
Event	2012 American Control Conference, ACC 2012 - Montreal, QC, Canada Duration: Jun 27 2012 → Jun 29 2012

Publication series

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

Other

Other	2012 American Control Conference, ACC 2012
Country/Territory	Canada
City	Montreal, QC
Period	6/27/12 → 6/29/12

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.1109/acc.2012.6315611

Cite this

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title = "An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints",

abstract = "In this paper, an efficient algorithm based on the ellipsoid method is proposed to solve a linear optimization problem over a set of uncertain Linear Matrix Inequalities (LMIs). First, an Ellipsoid Algorithm (EA) with deep cuts is introduced for solving the set of uncertain LMIs. The proposed ellipsoid algorithm is shown to converge to a probabilistically feasible point with high confidence level and in fewer iterations compared to other EA methods. Then, through a set of new cuts, the objective function is minimized while maintaining the probabilistic feasibility of the solution.",

author = "Armin Ataei and Qian Wang",

year = "2012",

doi = "10.1109/acc.2012.6315611",

language = "English (US)",

isbn = "9781457710957",

series = "Proceedings of the American Control Conference",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "857--862",

booktitle = "2012 American Control Conference, ACC 2012",

address = "United States",

note = "2012 American Control Conference, ACC 2012 ; Conference date: 27-06-2012 Through 29-06-2012",

}

Ataei, A & Wang, Q 2012, An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints. in 2012 American Control Conference, ACC 2012., 6315611, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 857-862, 2012 American Control Conference, ACC 2012, Montreal, QC, Canada, 6/27/12. https://doi.org/10.1109/acc.2012.6315611

An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints. / Ataei, Armin; Wang, Qian.
2012 American Control Conference, ACC 2012. Institute of Electrical and Electronics Engineers Inc., 2012. p. 857-862 6315611 (Proceedings of the American Control Conference).

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

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AU - Ataei, Armin

AU - Wang, Qian

PY - 2012

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N2 - In this paper, an efficient algorithm based on the ellipsoid method is proposed to solve a linear optimization problem over a set of uncertain Linear Matrix Inequalities (LMIs). First, an Ellipsoid Algorithm (EA) with deep cuts is introduced for solving the set of uncertain LMIs. The proposed ellipsoid algorithm is shown to converge to a probabilistically feasible point with high confidence level and in fewer iterations compared to other EA methods. Then, through a set of new cuts, the objective function is minimized while maintaining the probabilistic feasibility of the solution.

AB - In this paper, an efficient algorithm based on the ellipsoid method is proposed to solve a linear optimization problem over a set of uncertain Linear Matrix Inequalities (LMIs). First, an Ellipsoid Algorithm (EA) with deep cuts is introduced for solving the set of uncertain LMIs. The proposed ellipsoid algorithm is shown to converge to a probabilistically feasible point with high confidence level and in fewer iterations compared to other EA methods. Then, through a set of new cuts, the objective function is minimized while maintaining the probabilistic feasibility of the solution.

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DO - 10.1109/acc.2012.6315611

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SN - 9781457710957

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PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2012 American Control Conference, ACC 2012

Y2 - 27 June 2012 through 29 June 2012

ER -

An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints

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