## 1 Introduction  
With the rapid advancement of 5G network and Internet of Things (IoT), countless emerging mobile application scenarios have appeared in our lives, such as artificial intelligence, internet of vehicles, augmented reality, and virtual reality. This has led to the explosive growth of IoT devices such as smartphones, intelligent wireless sensors and wearable devices [1], and the amount of data processed by IoT devices has increased dramatically. All of these have put forward higher requirements for the real-time communication and computation capabilities of mobile devices. Some researchers have combined cloud computing with mobile computing to solve the problem of limited mobile device resources. Mobile cloud computing reduces the task burden of devices by migrating some or all of the computation tasks from resource-limited mobile devices to remote clouds [2; 3]. However, the disadvantages of this architecture are high overhead and long backhaul delay [4], and it is limited by network bandwidth. To solve this problem, a computing model called mobile edge computing (MEC) has received widespread attention from both industry and academia. The MEC server provides computation and storage resources for mobile devices at the edge of the network, and computation tasks can be offloaded to the edge of the network for execution, which can significantly reduce latency and reduce battery energy consumption [5]. Although MEC provides powerful computation resources for mobile devices, it still faces the challenge of limited battery energy supply. Obviously, frequent battery replacement and charging of wireless devices have brought huge costs. The emergence of wireless power transfer (WPT) technology has effectively solved the problem of insufficient energy supply of equipment. This technology broadcasts energy through radio frequency (RF) signals provided by energy transmitters to provide sustainable and permanent energy supply for mobile devices [6]. Recently, Wireless Powered Communication Network (WPCN) and Simultaneous Wireless Information and Power Transfer (SWIPT) have been proposed as important paradigms for providing real sustainability for mobile communications [7; 8]. The benefits of combining WPT and MEC have been fully demonstrated in recent years. This new technology is called wireless powered MEC (WP-MEC) [9]. This paper studies the residual energy maximization problem in an environment of MEC system integrating MEC server, Access Point (AP) and multiuser. AP can deliver energy to users through radio frequency (RF). The user converts the harvested energy, stores it in the battery, and uses the harvested energy to execute corresponding computation-intensive tasks. We achieve data and energy transmission in the same frequency band through Time Division Duplex (TDD) protocol. In addition, mobile devices transmit data in FDMA manner. In this paper, we focus on jointly optimizing the wireless and computation resources for the partial computation offloading system. The main contributions of this paper are detailed as follows:  
1. To effectively reduce the energy consumption of mobile devices, we study the multi-user dynamic joint optimization under multiple time blocks in the residual energy maximization problem. We jointly optimize the number of offloaded bits, energy harvesting time, and transmission bandwidth. To the best of our knowledge, in multiuser systems, most of the literature only studies the problem of active multiple users offloading and wireless energy transmission during one time block, and there are few works on dynamic joint optimization problems under multiple time blocks. 2. To solve the residual energy maximization problem of joint optimization, we propose a combined method of Bisection method and sequential unconstrained minimization based on reformulation linearization technique (RLT). We firstly derive the dual problem of the primary problem in a semi-closed form.