<p>This paper presents robust broadband beamforming design framework based on a semi-definite programming optimization strategy. To address sensor mismatches, the beamformer response is reformulated using a matrix quadratic form, thereby enabling the derivation of a worst-case performance upper bound. The proposed method using the proposed strategy accommodates both bounded perturbation mismatches and low-order statistical mismatches, offering a unified optimization formulation. Compared with second-order cone programming based methods, the proposed formulation provides a tighter convex relaxation and less sensitivity to mismatch parameter selection, mitigating over-constraint issues and enhancing robustness. Simulation results corroborate the effectiveness of the proposed approach, demonstrating superior robustness and passband response fidelity. Theoretical analysis underscores the pivotal role of the optimization strategy in achieving enhanced broadband beamformer performance, particularly in balancing robustness and frequency invariance through its influence on prior mismatch information.</p>