THE PROJECTION NEURAL NETWORK METHOD AND THE EULER METHOD FOR SOLVING THE SDLCP

This work introduces an innovative neural network based on projection techniques to address the Semi-Definite Linear Complementarity Problem (SDLCP). The SDLCP arises frequently in fields such as optimization theory, economic modeling, engineering computations, and operational analysis. From a theoretical standpoint, it is proven that, under appropriate assumptions, the developed method guarantees both the existence and uniqueness of solutions, alongside ensuring asymptotic and exponential stability. The continuous-time model is discretized using the explicit Euler scheme, and its convergence properties are rigorously established. To validate the proposed projection-based neural network approach and the discretization scheme, various MATLAB numerical tests are conducted. The designed neural network presents a viable and effective strategy for tackling SDLCP, showcasing considerable promise for practical deployment across disciplines.