Supervised learning of convex piecewise linear approximations of optimization problems

We propose to use input convex neural networks (ICNN) to build convex approximations of non-convex feasible sets of optimization problems, in the form of a set of linear equalities and inequalities in a lifted space. Our approach may be tailored to yield both inner- and outer- approximations, or to maximize its accuracy in regions closer to the minimum of a given objective function. We illustrate the method on two-dimensional toy problems and motivate it by various instances of reliability management problems of large-scale electric power systems.