A new approach to multicriterion optimization problem and its application to the design of 1-D digital filters

A novel method is presented for generating efficient points for the multicriterion optimization (MCO) problem. A novel function, the shifted minimax function, is defined that has the property that any efficient point of the MCO problem can be generated by minimizing the function with appropriately chosen shifts. Using this shifted minimax function for generating efficient points, the optimality conditions for the MCO problem have been derived. The method is also applied to the simultaneous amplitude and group delay approximation problem of 1-D digital filters