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The present methods for obtaining the optimal Lewenestein- Sanperadecomposition of a mixed state are difficult to handle analytically. We providea simple analytical expression for the optimal Lewenstein-Sanpera decompositionby using semidefinite programming. Specially, we obtain the optimalLewenstein-Sanpera decomposition for some examples such as: Bell decomposablestate, 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.

BEST SEPARABLE APPROXIMATION WITH SEMI-DEFINITE PROGRAMMING METHOD