Many technical issues for communications and computer infrastructures, including resource sharing, network management and distributed analytics, can be formulated as optimization problems. Gradient-based iterative algorithms have been widely utilized to solve these problems. Much research focuses on improving the iteration convergence. However, when system parameters change, it requires a new solution from the iterative methods. Therefore, it is helpful to develop machine-learning solution frameworks that can quickly produce solutions over a range of system parameters. We propose here a learning approach to solve non-convex, constrained optimization problems. Two coupled Long Short Term Memory (LSTM) networks are used to find the optimal solution. The advantages of this new framework include: (1) near optimal solution for a given problem instance can be obtained in very few iterations (time steps) during the inference process, (2) the learning approach allows selections of various hyper-parameters to achieve desirable tradeoffs between the training time and the solution quality, and (3) the coupled-LSTM networks can be trained using system parameters with distributions different from those used during inference to generate solutions, thus enhancing the robustness of the learning technique. Numerical experiments using a dataset from Alibaba reveal that the relative discrepancy between the generated solution and the optimum is less than 1% and 0.1% after 2 and 12 iterations, respectively.