Principal Component Pursuit Matrix Optimization Problem

Hi all

How can I solve this problem

let say A is any matrix

then minimize |L|+lambda||S|| subject to L+S=A.

where L is a low rank matric and S is a sparse matrix..The superposition of L and S gives the original matrice A

[Matt J]

What does the || operator signify? Absolute value? Frobenius or some other norm? Determinant?

Also, what are the unknowns? All elements of L and S? If all matrix elements can be chosen freely (apart from the constraint L+S=A), what is to ensure that L will be low rank and what is to ensure that S will be sparse?