Linearization of Problem on Placing a Maximum- Radius Hypersphere in Polyhedral Region

Abstract

The article provides analysis of a model on determining the maximum radius of hypersphere placed (immersed) into a polyhedral region (a convex set restricted by straight lines) with account taken of a set of factors including the following: Project Integration Management; Project Scope Management, Project Quality Management Project Time Management, Project Cost Management, Project Communication Management, Project Procurement Management and Project Risk Management. The model has proposed rigorous mathematic reduction (linearization) of a nonlinear optimization problem on placing a maximum-radius hypersphere into a convex polyhedral region, to a linear optimization problem. The proposed approach is generalized on an arbitrary finite dimensionality problem.