  We study how to solve semidefinite programming relaxations for large scale
polynomial optimization. When interior-point methods are used, typically only
small or moderately large problems could be solved. This paper studies
regularization methods for solving polynomial optimization problems. We
describe these methods for semidefinite optimization with block structures, and
then apply them to solve large scale polynomial optimization problems. The
performance is tested on various numerical examples. By regularization methods,
significantly bigger problems could be solved on a regular computer, which is
almost impossible by interior point methods.
