This work presents a data-driven optimization technique for the optimization of the flame response within a low-order acoustic network model. The methodology exploits the Nyquist criterion to compute a measure of thermoacoustic robustness at targeted frequencies, which serves as an objective value for the optimized system. The method is demonstrated using a simple Rijke tube model coupled with a -equation solver to model flame dynamics. The approach is shown to efficiently increase the stability margin of the system by modifying the flame transfer function. The methodology is applied to two examples, based on which possible scenarios are discussed and the potential and limitations associated with the practical implementation of the method are analyzed.