In this paper, we formalize an optimization framework for analog beamforming in the context of monostatic integrated sensing and communication (ISAC), where we also address the problem of self-interference in the analog domain. As a result, we derive semidefinite programs to approach detection-optimal transmit and receive beamformers, and we devise a superiorized iterative projection algorithm to approximate them. Our simulations show that this approach outperforms the detection performance of well-known design techniques for ISAC beamforming, while it achieves satisfactory self-interference suppression.