<p>In array signal processing, some beamforming algorithms require strict prior conditions on the mainlobe width. Therefore, this paper proposes a sparse optimization-based beamforming scheme, namely the minimum mainlobe width algorithm, addressing the high prior requirements on the mainlobe width imposed by some beamforming algorithms. Firstly, the problem of determining the mainlobe width is modeled, and a relaxation function is constructed. By introducing a set of constraints to the relaxation function, it is transformed into a sparse non-convex optimization problem. This transformation ensures that minimizing the mainlobe width is equivalent to minimizing the relaxation function under certain conditions. On this basis, the use of a sparse-excited log-sum-exp function further transforms the sparse non-convex optimization into a novel convex optimization problem, rendering it solvable. Consequently, the algorithm yields the minimum value of the mainlobe width determined by the weight vector. The proposed algorithm does not necessitate strict prior conditions on the mainlobe or sidelobe widths, enabling automatic determination of the minimum mainlobe width. Simulation results conducted in both linear and nonlinear array scenarios demonstrate the effectiveness of the algorithm in beamforming.</p>