In this paper, we consider the optimal approximations of univariate functions with feed-forward ReLU neural networks. We attempt to answer following questions. For given function and network, what is minimal possible approximation error? How fast does error decrease network size? Is attainable by current training techniques? Theoretically, introduce necessary sufficient conditions for convex fu...

Abstract We present a novel approach for approximating the primal and dual parameter-dependent solution functions of parametric optimization problems. start with an equation reformulation first-order necessary optimality conditions. Then, we replace solutions some find test parameters optimal coefficients as single nonlinear least-squares problem. Under mild assumptions it can be shown that sta...