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：求解带约束的非线性优化问题（CNLPs）是经济学、计算机科学和工程学等多个领域长期存在的难题。本文提出优化引导神经网络（OINN），一种基于深度学习求解CNLPs的方法。通过神经动力学优化方法，首先将CNLP转化为包含常微分方程组（ODE）的初值问题（IVP），然后利用神经网络模型作为该IVP的近似解，并将端点作为CNLP的预测结果。我们提出一种新型训练算法，引导模型在训练过程中保持最优预测。简而言之，OINN将CNLP转化为神经网络训练问题。通过这种方式，我们仅基于深度学习框架即可求解CNLP，无需使用标准优化求解器或数值积分求解器。通过一系列经典问题（例如变分不等式、非线性互补问题和标准CNLP）验证了该方法的有效性。