Degeneracy Graphs and Simplex Cycling

Inhaltsverzeichnis

• 1. Introduction.
• 2. Degeneracy problems in mathematical optimization.
• 2.1. Convergence problems in the case of degeneracy.
• 2.2 Efficiency problems in the case of degeneracy.
• 2.3 Degeneracy problems within the framework of postoptimal analysis.
• 2.4. On the practical meaning of degeneracy.
• 3. Theory of degeneracy graphs.
• 3.1. Fundamentals.
• 3.2 Theory of ? × n-degeneracy graphs.
• 3.3. Theory of 2 × n-degeneracy graphs.
• 4. Concepts to explain simplex cycling.
• 4.1. Specification of the question.
• 4.2 A pure graph theoretical approach.
• 4.3 Geometrically motivated approaches.
• 4.4 A determinant approach.
• 5. Procedures for constructing cycling examples.
• 5.1 On the practical use of constructed cycling examples.
• 5.2 Successive procedures for constructing cycling examples.
• 5.3 On the construction of general cycling examples.
• A. Foundations of linear algebra and the theory of convex polytopes.
• B. Foundations of graph theory.
• C. Problems in the solution of determinant inequality systems.
• References.