ISSN 1342-2804 Invariance under Affine Transformation in Semidefinite Programming Relaxation for Polynomial Optimization Problems
نویسندگان
چکیده
Given a polynomial optimization problem (POP), any affine transformation on its variable vector induces an equivalent POP. Applying Lasserre's SDP relaxation 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 affine transformation.
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