Optimization in Hilbert space by neural network approach

Based on linear programming neural networks, a neural network approach to optimization in Hilbert space is proposed. Rather than solving the optimization problems by computation in a digital computer, the authors obtain the answer by setting up the associated linear programming circuit and measured node voltages. This optimization net is simply a special-purpose analog computer which can solve the over-determined equation and its dual problem under-determined equation in L² space. Theoretical analysis and computer simulations show that the circuit to optimization in Hilbert space is guaranteed to settle into the correct answers within an RC time constant (on the order of several hundred nanoseconds), and has some advantages such as its normal and simple structure and tolerance of inaccuracies in the conductance matrix