Intelligent reflecting surface (IRS) is a promising new paradigm for enhancing wireless information transmission (WIT) and wireless power transfer (WPT) cost-effectively in the future. In this paper, we study an IRS-Aided full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid node (HN) operating in FD mode sends information signals to multiple devices in the downlink (DL), and meanwhile receives energy signals from a power station (PS) in the uplink (UL), both of which are assisted by an IRS. Our objective is to boost the weighted sum throughput by jointly optimizing the active transmit beamformer at the PS and HN, along with the passive reflection coefficients of the IRS. To deal with the formulated non-convex optimization problem with intricately coupled design variables, most of existing works employ the alternating optimization (AO) method, whose performance, however, is closely related to parameter initialization. In contrast, we develop two novel penalty-based algorithms for the single-device and multi-device cases, respectively. In particular, our proposed rank-one constraint reformulation method of matrix proves to be efficient, especially for the case where the objective function is a higher-order function of the IRS phase shifts. Numerical results demonstrate the superiority of our proposed design over benchmark schemes, and also unveil the necessity of the joint design of passive IRS beamforming and resource allocation for achieving better WPCN performance. Moreover, we draw useful insights into the fine-Tuning of IRS deployment location in the studied WPCN.