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Nonlinear projection equations (NPEs) provide a unified framework for solving various constrained nonlinear optimization and engineering problems. This paper presents a deep learning approach for solving NPEs by incorporating neurodynamic optimization and physics‐informed neural networks (PINNs). First, we model the NPE as a system of ordinary differential equations (ODEs) using neurodynamic optimization, and the objective becomes solving this ODE system. Second, we use a modified PINN to serve as the solution for the ODE system. Third, the neural network is trained using a dedicated algorithm to optimize both the ODE system and the NPE. Unlike conventional numerical integration methods, the proposed approach predicts the end state without computing all the intermediate states, resulting in a more efficient solution. The effectiveness of the proposed framework is demonstrated on a collection of classical problems, such as variational inequalities and complementarity problems. [ABSTRACT FROM AUTHOR]

This paper proposes a deep learning approach for solving non-smooth convex optimization problems (NCOPs), which have broad applications in computer science, engineering, and physics. Our approach combines neurodynamic optimization with physics-informed neural networks (PINNs) to provide an efficient and accurate solution. We first use neurodynamic optimization to formulate an initial value problem (IVP) that involves a system of ordinary differential equations for the NCOP. We then introduce a modified PINN as an approximate state solution to the IVP. Finally, we develop a dedicated algorithm to train the model to solve the IVP and minimize the NCOP objective simultaneously. Unlike existing numerical integration methods, a key advantage of our approach is that it does not require the computation of a series of intermediate states to produce a prediction of the NCOP. Our experimental results show that this computational feature results in fewer iterations being required to produce more accurate prediction solutions. Furthermore, our approach is effective in finding feasible solutions that satisfy the NCOP constraint. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel deep learning approach for predicting saddle points in stochastic two-player zero-sum games. Our method combines neurodynamic optimization and deep neural networks. First, we model the stochastic two-player zero-sum game as an ordinary differential equation (ODE) system using neurodynamic optimization. Second, we develop a neural network to approximate the solution to the ODE system, which includes the saddle point prediction for the game problem. Third, we introduce a specialized algorithm for training the neural network to enhance the accuracy of the saddle point prediction. Our experiments demonstrate that our model outperforms existing approaches, yielding faster convergence and more accurate saddle point predictions. [ABSTRACT FROM AUTHOR]