Abstract
The separation of two polyhedra by a family of parallel hyperplanes is a well-known problem with important applications in operations research,statistics and functional analysis. In this paper, we introduce a new algorithm for constructing a family of parallel hyperplanes that separates two disjoint polyhedra given by a system of linear inequalities.
To do this, we consider the alternative system and introduce its dual problem using the alternative theorem. We can find its minimum-norm solution by combining the objective function and constraints into a penalty function.
Since our objective function is only once differentiable, we propose an extension of Newton's method to solve the unconstrained objective optimization. The computational outcomes demonstrate the efficacy of the proposed method.