Convex cones, polyhedral sets and polytopes applied to linear systems and linear programming

This study, explores the subject of convex cones, polyhedral sets, polytopes and their relationship to linear systems and linear programming. This paper begins with the theory of convex sets. At this point necessary definitions, examples, and theorems of convexity are stated. These theorems and definitions are then used to introduce various classes of convex cones and their application to linear systems. Specifically, polyhedral cones are discussed in depth. These preliminary results are then applied to polyhedral sets and polytopes and their application to linear programming.