To achieve high gain and strong directivity,array antennas are widely used. As their core technology,beamforming plays a crucial role in suppressing sidelobe levels,expanding angle coverage,and enhancing anti-interference capabilities. Among various methods,convex optimization has become an effective approach for implementing complex beamforming (such as flat-top beams) due to its strong ability to handle multiple constraints and efficient solving characteristics. This paper proposes an efficient convex optimization method for flat-top beamforming of spherical cap arrays. The method first applies constraints in the main lobe"s target coverage area (approximately an arc-shaped region) to obtain an initial solution. Then,it performs iterative optimization by introducing specific constraint transformation strategies (e.g.,using absolute value operations to handle phase uncertainty),which significantly reduces computational complexity. Furthermore,an angle-domain non-uniform sampling strategy is adopted to reduce the number of optimization variables. Theoretical analysis and simulation experiments show that compared with traditional methods,the proposed method can effectively suppress gain fluctuations in the main lobe region of the beam pattern,significantly shorten the computation time,and improve the shaping efficiency.