Cones.jl

This package provides functionality related to polyhedral cones and polytopes. It's main purpose is to provide utilties for the package TailRiskScenGen.jl. It contains the following functionality:

• Provides type PolyhedralCone to represent cone defined by linear inequalities
• Provides type FiniteCone to represent cone defined by extremal rays
• Provides type Polytope to represent a polytope defined by extremal points and rays
• Implementation of Chernikova's algorithm which can be used to convert a PolyhedralCone to a FiniteCone
• Function to calculate extremal rays and points of a polytope defined by linear inequalities
• Functions to calculate projections of points onto polyhedral cones

Algorithms

• N.V. Chernikova, Algorithm for finding a general formula for the non-negative solutions of a system of linear inequalities, USSR Computational Mathematics and Mathematical Physics, Volume 5, Issue 2, 1965, Pages 228-233, https://doi.org/10.1016/0041-5553(65)90045-5.
• Fernandez, Felipe & Quinton, Patrice. (1988). Extension of Chernikova's algorithm for solving general mixed linear programming problems.

Acknowledgements

This project makes uses code from the Siconos Numerics project (http://siconos.gforge.inria.fr/) developed by INRIA for solving linear complementarity complementarity problems using Lemke's algorithm.