Joint admission control and power minimization are critical challenges in intelligent reflecting surface (IRS)-assisted networks. Traditional methods often rely on \( l_1 \)-norm approximations and alternating optimization (AO) techniques, which suffer from high computational complexity and lack robust convergence guarantees. To address these limitations, we propose a sigmoid-based approximation of the \( l_0 \)-norm AC indicator, enabling a more efficient and tractable reformulation of the problem. Additionally, we introduce a penalty dual decomposition (PDD) algorithm to jointly optimize beamforming and admission control, ensuring convergence to a stationary solution. This approach reduces computational complexity and supports distributed implementation. Moreover, it outperforms existing methods by achieving lower power consumption, accommodating more users, and reducing computational time.