In this paper, we study the distributed cooperative optimization problem with globally equality and inequality constraints for a multi-agent system, where each agent is modeled by Euler-Lagrangian (EL) dynamics. The optimized function can be represented by the sum of all local cost functions corresponding to each individual agent. Two continuous-time algorithms are proposed to solve such the problem in a distributed manner. In virtue of geometric graph theory, convex analysis, and Lyapunov stability theory, it is proved that all agents achieve consensus on the Lagrangian multipliers associated with constraints while the proposed algorithms converge exponentially to the optimal solution of the problem given in the case that the parameters of EL agents are known, and converge asymptotically to the optimal solution of the problem in the case that the parameters of EL agents are unknown, respectively. Finally, an example is provided to demonstrate the effectiveness of the theoretical results.