Linear Programming Computation [electronic resource] /

Chapter 1. Introduction -- Chapter 2. Geometry of Feasible Region -- Chapter 3. Simplex Method -- Chapter 4. Implementation of Simplex Method -- Chapter 5. Duality Principle and Dual Simplex Method -- Chapter 6. Primal-Dual Simplex Method -- Chapter 7. Sensitivity Analysis and Parametric LP -- Chapter 8. Generalized Simplex Method -- Chapter 9. Decomposition Method -- Chapter 10. Interior-Point Method -- Chapter 11. Integer Linear Programming (ILP) -- Chapter 12. Pivot Rule -- Chapter 13. Dual Pivot Rule -- Chapter 14. Simplex Phase-I Method -- Chapter 15. Dual Simplex Phase-l Method -- Chapter 16. Reduced Simplex Method -- Chapter 17. D-Reduced Simplex Method -- Chapter 18. Generalized Reduced Simplex Method -- Chapter 19. Deficient-Basis Method -- Chapter 20. Dual Decient-Basis Method -- Chapter 21. Face Method with Cholesky Factorization -- Chapter 22. Dual Face Method with Cholesky Factorization -- Chapter 23. Face Method with LU Factorization -- Chapter 24. Dual Face Method with LU Factorization -- Chapter 25. Simplex Interior-Point Method -- Chapter 26. Facial Interior-Point Method -- Chapter 27. Decomposition Principle.

Organized into two volumes. this book represents a real breakthrough in the field of linear programming (LP). The first volume addresses fundamentals, including geometry of feasible region, simplex method, implementation of simplex method, duality and dual simplex method, sensitivity analysis and parametric LP, generalized simplex method, decomposition method, interior-point method and integer LP method, as well as reflects the state of art by highlighting new results, such as efficient primal and dual pivot rules, primal and dual Phase-I methods. The second volume introduces contributions of the author himself, such as reduced and D-reduced-simplex methods, generalized reduced and dual reduced simplex methods, deficient-basis and dual deficient-basis-simplex methods, and face and dual face methods with Cholesky factorization, as well as with LU factorization. As a monograph, this book is a rare work in LP, containing many noval ideas and methods, supported by complete computational results. As revealed from the perspective of theory, the most recently achieved results, such as reduced and D-reduced simplex methods, as well as ILP solvers--- controlled-cut and controlled-branch methods, are very significant and promising, though there are no computational results available at this stage. With a focus on computation, the content of this book ranges from simple to profound, clear and fresh. In particular, all algorithms are accompanied by examples for demonstration whenever possible. As a milestone of LP, this book is an indispensable tool for undergraduate and graduate students, teachers, practitioners and researchers, in LP and related fields.