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A modified version of the method of moving asymptotes is proposed based on the spectral parameter used in the updating of a key parameter of the model. The second-order information present in the spectral parameter is thus included in the model functions that define the rational approximations. Numerical experiments indicate that the idea is promising in the sense that the cost-benefit of computing the spectral parameter is worth it for reducing the total effort of the algorithm when compared with the original version. [ABSTRACT FROM AUTHOR]