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The proposed new minimax design method for 2D FIR filters is based on sequential quadratic programming (SQP). The main reason to formulate and solve the design problem in an SQP formulation is that the complementarity conditions associated with the SQP lead to a very small number of nonzero Lagrange multipliers that need to be updated in a given iteration. This in turn improves design efficiency as well as the algorithm's numerical stability, which is of critical importance as both the number of design variables and the constraints involved in a 2D design are much higher than a 1D design. Design examples with comparisons are presented to illustrate the effectiveness of the proposed method.