To address the problem of optimal rendezvous for multiple unmanned aerial vehicles (UAVs) within a given time frame, a distributed optimization approach was investigated for developing a control algorithm that enabled UAVs to achieve optimal rendezvous in a directed communication network with unbalanced weights. Each UAV was associated with a local objective function, and the global objective function was defined as the sum of the local objective functions of all UAVs. The aim of the algorithm was to find the optimal rendezvous point that satisfies the global objective function through distributed control. Inspired by the concept of temporal mapping, the given time-constrained rendezvous problem was transformed into an unconstrained rendezvous problem in infinite time domain, overcoming the imbalance in the directed network by utilizing the left eigenvectors corresponding to the zero eigenvalue of the Laplacian matrix. By combining convex analysis theory and Lyapunov stability theory, the algorithm's convergence to the optimal solution was validated. Simulation results demonstrate that UAVs with different initial positions can reach the optimal rendezvous point within the given time frame under the control of the proposed algorithm.