Properties, Extensions and Application of Piecewise Linearization for Euclidean Norm Optimization in R 2

This work considers non-convex mixed integer nonlinear programming where nonlinearity comes from the presence of the two-dimensional euclidean norm in the objective or the constraints. We build from the euclidean norm piecewise linearization proposed by Camino et al. [2019], that allows to solve such non-convex problems via mixed-integer linear programming with an arbitrary approximation guarantee. Theoretical results are established that prove that this linearization is able to satisfy any given approximation level with the minimum number of pieces. Anextension of the piecewise linearization approach is proposed. It shares the same theoretical properties for elliptic constraints and/or objective.An application shows the practical appeal of the elliptic linearization on a non-convex beam layout mixed optimization problem coming from an industrial application