This paper studies the distributed resource allocation problem with convex inequality constraints over the multi-agent systems. The local cost function and convex inequality constraints are known by themselves of each agent in the resource allocation problem. The aim of the distributed resource allocation problem is how to design a distributed optimization algorithm by using the information exchange between neighboring agents while minimizing the global cost functions. For this problem, based on the Karush-Kuhn-Tucker condition and proportional integral control idea, we firstly propose an adaptive distributed optimization algorithm, using which the dual variable of the inequality is obtained adaptively. Then, to reduce the communication resource consumption of the system, the discrete-time communication of the distributed resource allocation algorithm is realized by designing a dynamic event-triggered control scheme. Finally, the numerical simulation shows the effectiveness of the proposed algorithms.