In this paper the design of power system shunt filters to ensure harmonic reduction and noise mitigation on the electrical utility grid is formulated as an optimization problem. The proposed filter design technique ensures the most economic filter design, and deviates from the common design practise of dedicating specific filters to designated harmonic interfering orders. It is based on the minimization of the L(infinity)-norm, over a specified continuous interfering frequency range, of a composite user specified objective function depicting the three main filter objectives of low harmonic injection into the AC host utility grid, maximum absorption by the harmonic filter and minimum harmonic voltage distortion at the point of common coupling (PCC). In addition to these objectives, near parallel resonance conditions on the combined system/filter configuration are to be avoided. These conditions are included in the formulation of the optimization problem as a functional inequality constraint over the specified continuous frequency range. The problem is approximated by a sequence of optimization problems which are readily solved using standard software packages. A representative filter design problem is solved to illustrate the proposed method.