A neurodynamic method (NdM) for convex optimization is proposed in this paper with an equality constraint. The method utilizes a neurodynamic system (NdS) that converges to the optimal solution of a convex optimization problem in a fixed time. Due to its mathematical simplicity, it can also be combined with reinforcement learning (RL) to solve a class of nonconvex optimization problems. To maintain the mathematical simplicity of NdS, zero-sum initial constraints are introduced to reduce the number of auxiliary multipliers. First, the initial sum of the state variables must satisfy the equality constraint. Second, the sum of their derivatives is designed to remain zero. In order to apply the proposed convex optimization algorithm to nonconvex optimization with mixed constraints, the virtual actions in RL are redefined to avoid the use of NdS inequality constrained multipliers. The proposed NdM plays an effective search tool in constrained nonconvex optimization algorithms. Numerical examples demonstrate the effectiveness of the proposed algorithm.