A method to solve a general broadband beamformer design problem is formulated as a quadratic program. As a special case, the minimax near-field design problem of a broadband beamformer is solved as a quadratic programming formulation of the weighted Chebyshev approximation problem. The method can also be applied to the design of multidimensional digital FIR filters with an arbitrarily specified amplitude and phase. For linear phase multidimensional digital FIR filters, the quadratic program becomes a linear program. Examples are given that demonstrate the minimax near-field behavior of the beamformers designed.