Linear and nonlinear programming
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Bibliographic Information
Linear and nonlinear programming
Kluwer Academic, c2003
2nd ed
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Includes bibliographical references and index
Description and Table of Contents
Description
The original edition of this book was celebrated for its coverage of the central concepts of practical optimization techniques. This updated edition expands and illuminates the connection between the purely analytical character of an optimization problem, expressed by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. Incorporating modern theoretical insights, this classic text is even more useful.
Table of Contents
1. Introduction.
Part I: Linear Programming. 2. Basic Properties of Linear Programs.3. The Simplex Method. 4. Duality. 5. Transportation and Network Flow Problems.
Part II: Unconstrained Problems. 6. Basic Properties of Solutions and Algorithms. 7. Basic Descent Methods. 8. Conjugate Direction Methods. 9. Quasi- Newton Methods.
Part III: Constrained Minimization. 10. Constrained Minimization Conditions. 11. Primal Methods. 12. Penalty and Barrier Methods. 13. Dual and Cutting Plane Methods. 14. Lagrange Methods.
Appendix A: Mathematical Review. A.1. Sets. A.2. Matrix Notation. A.3. Spaces. A.4. Eigenvalues and Quadratic Forms. A.5. Topological Concepts. A.6. Functions.
Appendix B: Convex Sets. B.1. Basic Definitions. B.2. Hyperplanes and Polytopes. B.3. Separating and Supporting Hyperplanes. B.4. Extreme Points.
Appendix C: Gaussian Elimination.
Bibliography. Index.
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