Invariance under affine transformation in semidefinite programming relaxation for polynomial optimization problems

Hayato Waki, Masakazu Muramatsu, Masakazu Kojima

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Given a polynomial optimization problem (POP), any nonsingular affine transformation on its variable vector induces an equivalent POP. Applying Lasserre's SDP relaxation [SIAM J.Opt. 11:796-817, 2001] to the original and the transformed POPs, we have two SDPs. This paper shows that these two SDPs are isomorphic to each other under a nonsingular linear transformation, which maps the feasible region of one SDP onto that of the other isomorphically and preserves their objective values. This fact means that the SDP relaxation is invariant under any nonsingular affine transformation.

Original languageEnglish
Pages (from-to)295-310
Number of pages16
JournalPacific Journal of Optimization
Volume5
Issue number2
Publication statusPublished - May 1 2009

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Semidefinite Programming Relaxation
Invariance
Affine transformation
Polynomials
Optimization Problem
Linear transformations
Polynomial
Feasible region
Linear transformation
Isomorphic
Invariant

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Cite this

Invariance under affine transformation in semidefinite programming relaxation for polynomial optimization problems. / Waki, Hayato; Muramatsu, Masakazu; Kojima, Masakazu.

In: Pacific Journal of Optimization, Vol. 5, No. 2, 01.05.2009, p. 295-310.

Research output: Contribution to journalArticle

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