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.
|Number of pages||16|
|Journal||Pacific Journal of Optimization|
|Publication status||Published - May 1 2009|
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Computational Mathematics
- Applied Mathematics