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The Lagrange multiplier method is one of the basic optimization procedures to find the optimum polarizations for the incoherent scattering case. This letter proves for the first time that a fixed relationship exists between the optimum polarization and the Lagrange multiplier. Then, an optimization procedure is proposed to simplify the computational complexity of the Lagrange multiplier method. To speed up the convergence of the proposed procedure, the minimum search intervals are discussed and given theoretically. A numerical example is shown to demonstrate the effectiveness of the proposed procedure.