Simplicial Algorithms on the Simplotope

I Introduction and Definitions.- 1. Introduction.- 1.1. Introduction.- 1.2. Historical perspective.- 1.3. Outline of the monograph.- 2. Definitions and Existence Theorems.- 2.1. Introduction.- 2.2. Basic concepts and notations.- 2.3. Existence theorems.- 2.4. Labelling functions and accuracy.- 2.5. Pure exchange economies.- 2.6. Quadratically constrained quadratic programming.- 2.7. Economies with a block diagonal supply-demand pattern.- 2.8. Noncooperative N-person games.- 3. Triangulations of Sn and S.- 3.1. Introduction.- 3.2. The Q-triangulation of Sn and S.- 3.3. The Q’-triangulation of S.- 3.4. The V-triangulation of Sn.- 3.5. The V’- and the V-triangulation of S.- 3.6. Variants of the V-triangulation.- II Algorithms on the Unit Simple.- 4. An introduction to Simplicial Algorithms on the Unit Simplex.- 4.1. Introduction.- 4.2. The variable dimension restart algorithm on Sn for proper integer labelling rules.- 4.3. Variable dimension restart algorithms on Sn for arbitrary integer labelling rules.- 4.4. Variable dimension restart algorithms on Sn for vector labelling.- 4.5. A path following interpretation of the variable dimension restart algorithm for the V-triangulation.- 5. The (2n+1-2)-Ray Algorithm.- 5.1. Introduction.- 5.2. The path of the algorithm.- 5.3. The subdivision of Sn.- 5.4. The steps of the algorithm.- 6. The 2-Ray Algorithm.- 6.1. Introduction.- 6.2. The path of the algorithm.- 6.3. The subdivision of Sn.- 6.4. The steps of the algorithm.- 7. Comparisons and Computational Results.- 7.1. Introduction.- 7.2. A comparison of the variable dimension restart algorithms on Sn.- 7.3. Computational results.- III Algorithms on the Simplotope.- 8. An Introduction to Simplicial Algorithms on the Simplotope.- 8.1. Introduction.- 8.2. The sum-ray algorithm on S for proper integer labelling rules.- 8.3. Variable dimension restart algorithms on S for arbitrary integer labelling rules.- 8.4. The sum-ray algorithm on S for vector labelling.- 8.5. A path following interpretation of the sum-ray algorithm for the V’ -triangulation.- 9. The Product-Ray Algorithm.- 9.1. Introduction.- 9.2. The path of the algorithm.- 9.3. The subdivision of S.- 9.4. The steps of the algorithm.- 10. The Exponent-Ray Algorithm.- 10.1. Introduction.- 10.2. The path of the algorithm.- 10.3. The subdivision of S.- 10.4. The steps of the algorithm.- 11. Comparisons and Computational Results.- 11.1. Introduction.- 11.2. A comparison of the variable dimension restart algorithms on S.- 11.3. Computational results.- IV Continuous Deformation on the Simplotope.- 12. The Continuous Deformation Algorithm on the Simplotope.- 12.1. Introduction.- 12.2. The path of the algorithm.- 12.3. Triangulation of S x [1,?).- 12.4. Triangulation of the boundary of S x [1, ?).- 12.5. The steps of the continuous deformation algorithm on S.- References.