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A passive filter often becomes a key component for the communication system. The optimization design of passive filter is the most effective procedure in performance improving. In this paper, the formula of calculating the gradient vector and the Hessian matrix is presented. Based on this formula, the optimization for the objective function in the problem of lossy filter design is derived and then the circuit optimization technique is extended into with the composing optimization algorithms suitable. The flexibility and effectiveness of this technique to passive filter design is proved with examples given.