Beam Hopping (BH) is a popular technique considered for next-generation multi-beam satellite communication system which allows a satellite focusing its resources on where they are needed by selectively illuminating beams. While beam illumination plan can be adjusted according to its needs, the main limitation of convectional BH is the adjacent beam avoidance requirement needed to maintain acceptable levels of interference. With the recent maturity of precoding technique, a natural way forward is to consider a dynamic beam illumination scheme with selective precoding, where large areas with high-demand can be covered by multiple active precoded beams. In this paper, we mathematically model such beam illumination design problem employing an interference-based penalty function whose goal is to avoid precoding whenever possible subject to beam demand satisfaction constraints. The problem can be written as a binary quadratic programming (BQP). Next, two convexification frameworks are considered namely: (i) A Semi-Definition Programming (SDP) approach particularly targeting BQP type of problems, and (ii) Multiplier Penalty and Majorization-Minimization (MPMM) based method which guarantees to converge to a local optimum. Finally, a greedy algorithm is proposed to alleviate complexity with minimal impact on the final performance. Supporting results based on numerical simulations show that the proposed schemes outperform the relevant benchmarks in terms of demand matching performance while minimizing the use of precoding.