  The present methods for obtaining the optimal Lewenestein- Sanpera
decomposition of a mixed state are difficult to handle analytically. We provide
a simple analytical expression for the optimal Lewenstein-Sanpera decomposition
by using semidefinite programming. Specially, we obtain the optimal
Lewenstein-Sanpera decomposition for some examples such as: Bell decomposable
state, Iso-concurrence state, generic two qubit state in Wootters's basis,
$2\otimes 3$ Bell decomposable state, $d\otimes d$ Werner and isotropic states,
a one parameter $3\otimes 3$ state and finally multi partite isotropic state.
