A numerical algorithm for block-diagonal decomposition of matrix -algebras with application to semidefinite programming

Kazuo Murota, Yoshihiro Kanno, Masakazu Kojima, Sadayoshi Kojima

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

Motivated by recent interest in group-symmetry in semidefinite programming, we propose a numerical method for finding a finest simultaneous block-diago- nalization of a finite number of matrices, or equivalently the irreducible decomposition of the generated matrix *-algebra. The method is composed of numerical-linear algebraic computations such as eigenvalue computation, and automatically makes full use of the underlying algebraic structure, which is often an outcome of physical or geometrical symmetry, sparsity, and structural or numerical degeneracy in the given matrices. The main issues of the proposed approach are presented in this paper under some assumptions, while the companion paper gives an algorithm with full generality. Numerical examples of truss and frame designs are also presented.

Original languageEnglish
Pages (from-to)125-160
Number of pages36
JournalJapan Journal of Industrial and Applied Mathematics
Volume27
Issue number1
DOIs
Publication statusPublished - 2010 Jun 1
Externally publishedYes

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Semidefinite Programming
Matrix Algebra
Numerical Algorithms
Eigenvalue Computation
Decomposition
Decompose
Symmetry Group
Algebraic Structure
Degeneracy
Sparsity
Numerical Methods
Symmetry
Numerical Examples
Numerical methods
Design

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

Cite this

A numerical algorithm for block-diagonal decomposition of matrix -algebras with application to semidefinite programming. / Murota, Kazuo; Kanno, Yoshihiro; Kojima, Masakazu; Kojima, Sadayoshi.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 27, No. 1, 01.06.2010, p. 125-160.

Research output: Contribution to journalArticle

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