Properties, Extensions and Application of Piecewise Linearization for Euclidean Norm Optimization in $$\mathbb {R}^2$$

This work considers nonconvex mixed integer nonlinear programming where nonlinearity comes from the presence of two-dimensional euclidean norm in objective or constraints. We build piecewise linearization proposed by Camino et al. (Comput. Optim. Appl. https://doi.org/10.1007/s10589-019-00083-z , 2019) that allows to solve such problems via mixed-integer linear with an arbitrary approximation guarantee. Theoretical results are established prove this is able satisfy any given level minimum number pieces. An extension approach proposed. It shares same theoretical properties for elliptic constraints and/or objective. application shows practical appeal on a beam layout optimization problem coming industrial application.