Gradient-based iterative algorithms have been widely used to solve optimization problems, including resource sharing and network management. When system parameters change, it requires a new solution independent of the previous parameter settings from the iterative methods. Therefore, we propose a learning approach that can quickly produce optimal solutions over a range of system parameters for constrained optimization problems. Two Coupled Long Short-Term Memory networks (CLSTMs) are proposed to find the optimal solution. The advantages of this framework include: (1) near-optimal solution for a given problem instance can be obtained in few iterations during the inference, (2) enhanced robustness as the CLSTMs can be trained using system parameters with distributions different from those used during inference to generate solutions. In this work, we analyze the relationship between minimizing the loss functions and solving the original constrained optimization problem for certain parameter settings. Extensive numerical experiments using datasets from Alibaba reveal that the solutions to a set of nonconvex optimization problems obtained by the CLSTMs reach within 90% or better of the corresponding optimum after 11 iterations, where the number of iterations and CPU time consumption are reduced by 81% and 33%, respectively, when compared with the gradient descent with momentum.