A Finite Step Projective Algorithm for Solving Linear Matrix Inequalities

Robert Orsi; Mustapha Ait Rami; John B. Moore

A Finite Step Projective Algorithm for Solving Linear Matrix Inequalities

Robert Orsi^*, Mustapha Ait Rami, John B. Moore

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

7 Citations (Scopus)

Abstract

This paper presents an algorithm for finding feasible solutions of linear matrix inequalities. The algorithm is based on the method of alternating projections (MAP), a classical method for solving convex feasibility problems. Unlike MAP, which is an iterative method that converges asymptotically to a feasible point, the algorithm converges after a finite number of steps. The key computational component of the algorithm is an eigenvalue-eigenvector decomposition which is carried out at each iteration. Computational results for the algorithm are presented and comparisons are made with existing algorithms.

Original language	English
Pages (from-to)	4979-4984
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	5
Publication status	Published - 2003
Event	42nd IEEE Conference on Decision and Control - Maui, HI, United States Duration: 9 Dec 2003 → 12 Dec 2003

Cite this

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title = "A Finite Step Projective Algorithm for Solving Linear Matrix Inequalities",

abstract = "This paper presents an algorithm for finding feasible solutions of linear matrix inequalities. The algorithm is based on the method of alternating projections (MAP), a classical method for solving convex feasibility problems. Unlike MAP, which is an iterative method that converges asymptotically to a feasible point, the algorithm converges after a finite number of steps. The key computational component of the algorithm is an eigenvalue-eigenvector decomposition which is carried out at each iteration. Computational results for the algorithm are presented and comparisons are made with existing algorithms.",

author = "Robert Orsi and \{Ait Rami\}, Mustapha and Moore, \{John B.\}",

year = "2003",

language = "English",

volume = "5",

pages = "4979--4984",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0743-1546",

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

note = "42nd IEEE Conference on Decision and Control ; Conference date: 09-12-2003 Through 12-12-2003",

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TY - JOUR

T1 - A Finite Step Projective Algorithm for Solving Linear Matrix Inequalities

AU - Orsi, Robert

AU - Ait Rami, Mustapha

AU - Moore, John B.

PY - 2003

Y1 - 2003

N2 - This paper presents an algorithm for finding feasible solutions of linear matrix inequalities. The algorithm is based on the method of alternating projections (MAP), a classical method for solving convex feasibility problems. Unlike MAP, which is an iterative method that converges asymptotically to a feasible point, the algorithm converges after a finite number of steps. The key computational component of the algorithm is an eigenvalue-eigenvector decomposition which is carried out at each iteration. Computational results for the algorithm are presented and comparisons are made with existing algorithms.

AB - This paper presents an algorithm for finding feasible solutions of linear matrix inequalities. The algorithm is based on the method of alternating projections (MAP), a classical method for solving convex feasibility problems. Unlike MAP, which is an iterative method that converges asymptotically to a feasible point, the algorithm converges after a finite number of steps. The key computational component of the algorithm is an eigenvalue-eigenvector decomposition which is carried out at each iteration. Computational results for the algorithm are presented and comparisons are made with existing algorithms.

UR - https://www.scopus.com/pages/publications/1542289984

M3 - Conference article

AN - SCOPUS:1542289984

SN - 0743-1546

VL - 5

SP - 4979

EP - 4984

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - 42nd IEEE Conference on Decision and Control

Y2 - 9 December 2003 through 12 December 2003

ER -

A Finite Step Projective Algorithm for Solving Linear Matrix Inequalities

Abstract

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