This article studies a distributed constrained optimization problem of multiple agents characterized by Euler–Lagrange systems with unknown inertial parameters. The optimization objective is to compute a feasible solution within the intersection of a series of constrained sets such that a global payoff function summed by a group of local ones is minimized. Meanwhile, each local payoff function and constrained set are just privately available to their respective agent. To accomplish the concerned constrained optimization objective, a fully distributed continuous-time algorithm resorting to a projection-based auxiliary dynamics is synthesized without using global topology information. The proposed distributed optimization algorithm is privacy-preserving in the sense that no actual state information is exchanged between distinct agents during the seeking progress. Besides, the associated stability analysis is carried out in terms of the Lyapunov theorem. Finally, a source localization example is performed to verify the effectiveness of the proposed distributed optimization algorithm.