A Discrete-Time Neural Network for Optimization Problems With Hybrid Constraints

Recurrent neural networks have become a prominent tool for optimizations including linear or nonlinear variational inequalities and programming, due to its regular mathematical properties and well-defined parallel structure. This brief presents a general discrete-time recurrent network for linear variational inequalities and related optimization problems with hybrid constraints. In contrary to the existing discrete-time networks, this general model can operate not only on bound constraints, but also on hybrid constraints comprised of inequality, equality and bound constraints. The model has dynamical properties of global convergence, asymptotical and exponential convergences under some weaker conditions. Numerical examples demonstrate its efficacy and performance.