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The problem of tuning stabilizers in multimachine power systems has been formulated here as a sequence of optimization problems. Both quadratic and linear programming problems have been considered. In the former case, stabilizers with complex zeros have been included in the compensator model. In each case a particular measure of the stabilizers' gain has been defined. The constraints have been written to represent the region allowed for eigenvalue shifting together with specific constraints. The objective has been to shift the lightly damped eigenvalues associated to the system electromechanical modes. The results have shown that the quadratic programming formulation may be an important auxiliary tool for stabilizers tuning.