<p>Most of the all existing distributed finite/fixed/predefined-time optimization results are achieved through fractional power feedback, resulting in a fractional-power algorithm structure and complicated convergence analysis. For this reason, we design a distributed predefined-time zero-gradient-sum (ZGS) optimization algorithm by exploiting time-varying gain function. The proposed algorithm enjoys the following features: 1) the state feedback is direct and linear (thus the algorithm structure and the convergence analysis are more simple); 2) the convergence time can be preset based on the task demands; 3) the convergence time is irrelevant to the agent’s initial conditions and the control parameters. When considering the communication efficiency, we further design a distributed predefined-time ZGS algorithm without continuous-time communication by synthesizing the dynamic event-triggered mechanism and the time-varying gain function. The proposed algorithms exhibit simplicity in their structure and possess the advantage of fast convergence. Theoretical analysis and simulation results verify the feasibility of our proposed predefined-time algorithms.</p>