A new method for the design of spatial filters having flat response based on the semi-infinite optimization techniques is presented.The method is to minimize the array noise power subject to the linear functional inequality constraints

which ensure the flat response of the spatial filters in the interest of spatial sector. Because of the hard constraints

the response of the spatial filters can be controlled in the allowable errors.Finally

we study the flat-based estimation of direction-of-arrival of signals.Computer simulation results and analyses show the advantages of the proposed method over the other related methods.