This paper analyzes and optimizes the outage performance of multi-hop cognitive wireless powered networks (CWPNs) in underlay paradigms. To be specific, there are multiple power beacons (PBs) performing wireless power transfer (WPT) for multiple battery-free secondary users (SUs). Correspondingly, the SUs first harvest energy from the RF signals of PBs and then execute multi-hop cognitive data transmission in the licensed channel concurrently with the primary users (PUs). Therefore, the transmit power of SUs are subject to the energy causality constraint imposed by WPT and the interference power constraint from multiple PUs. We derive and obtain the closed-form exact and asymptotic end-to-end outage probabilities for multi-hop CWPNs over Rayleigh block fading. Furthermore, we optimize the outage performance by studying the outage minimization problem with respect to the WPT power and the WPT time. Due to the complexity of outage probability, we propose a self-adaptive particle swarm optimization (SA-PSO)-based resource allocation algorithm to jointly optimize the power and time for WPT. Extensive simulations validate the correctness of theoretical analysis and the effectiveness of the proposed optimization algorithm. INDEX TERMS Multi-hop, cognitive wireless powered networks, energy harvesting, outage probability, particle swarm optimization.