Solving constrained nonlinear optimization problems (CNLPs) is a longstanding problem that arises in various fields, e.g., economics, computer science, and engineering. We propose optimization-informed neural networks (OINN), a deep learning approach to solve CNLPs. By neurodynamic optimization methods, a CNLP is first reformulated as an initial value problem (IVP) involving an ordinary differential equation (ODE) system. A neural network model is then used as an approximate solution for this IVP, with the endpoint being the prediction to the CNLP. We propose a novel training algorithm that directs the model to hold the best prediction during training. In a nutshell, OINN transforms a CNLP into a neural network training problem. By doing so, we can solve CNLPs based on deep learning infrastructure only, without using standard optimization solvers or numerical integration solvers. The effectiveness of the proposed approach is demonstrated through a collection of classical problems, e.g., variational inequalities, nonlinear complementary problems, and standard CNLPs.

翻译：求解约束非线性优化问题（CNLP）是一个长期存在的难题，涉及经济学、计算机科学和工程学等多个领域。我们提出优化信息神经网络（OINN），这是一种解决CNLP的深度学习方法。通过神经动力学优化方法，CNLP首先被重述为一个包含常微分方程（ODE）系统的初值问题（IVP）。随后，利用神经网络模型作为该IVP的近似解，其终点即为对CNLP的预测。我们还提出了一种新颖的训练算法，引导模型在训练过程中保持最优预测。简言之，OINN将CNLP转化为神经网络训练问题。通过这种方式，我们仅依靠深度学习基础设施即可求解CNLP，无需使用标准优化求解器或数值积分求解器。通过对一系列经典问题（如变分不等式、非线性互补问题及标准CNLP）的测试，验证了该方法的有效性。