  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.
