In this paper we consider the intelligent reflecting surface (IRS) configuration under quality-of-service (QoS) constraints in the multi-user multi-input-single-output (MISO) uplink wireless network. Note that the IRS phase-shifting design under the IRS-dependent-QoS-constraints are generally very challenging and not widely considered in the existing literature. Utilizing the novel nonlinear equality constrained alternative direction method of multipliers (neADMM) framework, we develop a novel second-order-cone-programming (SOCP) solution to optimize the IRS configuration. Our method can effectively solve the feasibility check and weighted sum-power minimization in the aforementioned system setting. Extensive simulation results demonstrate that this newly designed algorithm outperforms the conventional methods like semidefinite relaxation (SDR) and the standard alternative direction method of multipliers (ADMM), which are now widely used in the existing literature.