The GroupMax Neural Network Approximation of Convex Functions.

We present a new neural network to approximate convex functions. This network has the particularity to approximate the function with cuts which is, for example, a necessary feature to approximate Bellman values when solving linear stochastic optimization problems. The network can be easily adapted to partial convexity. We give an universal approximation theorem in the full convex case and give many numerical results proving its efficiency. The network is competitive with the most efficient convexity-preserving neural networks and can be used to approximate functions in high dimensions.