Optimization is of central importance in all sciences. Nature inherently seeks optimal solutions. For example, light travels through the "shortest" path and the folded state of a protein corresponds to the structure with the "minimum" potential energy. In combinatorial optimization, there are numerous computationally hard problems arising in real world applications, such as floorplanning in VLSI designs and Steiner trees in communication networks. For these problems, the exact optimal solution is not currently real-time computable. One usually computes an approximate solution with various kinds of heuristics. Recently, many approaches have been developed that link the discrete space of combinatorial optimization to the continuous space of nonlinear optimization through geometric, analytic, and algebraic techniques. Many researchers have found that such approaches lead to very fast and efficient heuristics for solving large problems. Although almost all such heuristics work well in practice there is no solid theoretical analysis, except Karmakar's algorithm for linear programming. With this situation in mind, we decided to teach a seminar on nonlinear optimization with emphasis on its mathematical foundations. This book is the result of that seminar. During the last decades many textbooks and monographs in nonlinear optimization have been published. Why should we write this new one? What is the difference of this book from the others? The motivation for writing this book originated from our efforts to select a textbook for a graduate seminar with focus on the mathematical foundations of optimization.
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Preface. 1. Optimization Problems. 2. Linear Programming. 3. Blind Man's Method. 4. Hitting Walls. 5. Slope and Path Length. 6. Average Slope. 7. Inexact Active Constraints. 8. Efficiency. 9. Variable Metric Methods. 10. Powell's Conjecture. 11. Minimax. 12. Relaxation. 13. Semidefinite Programming. 14. Interior Point Methods. 15. From Local to Global. Historical Notes. Bibliography. Index.
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Opti. Codice articolo 4175528
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Optimization includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems. 292 pp. Englisch. Codice articolo 9781441952028
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - Optimization is of central importance in all sciences. Nature inherently seeks optimal solutions. For example, light travels through the 'shortest' path and the folded state of a protein corresponds to the structure with the 'minimum' potential energy. In combinatorial optimization, there are numerous computationally hard problems arising in real world applications, such as floorplanning in VLSI designs and Steiner trees in communication networks. For these problems, the exact optimal solution is not currently real-time computable. One usually computes an approximate solution with various kinds of heuristics. Recently, many approaches have been developed that link the discrete space of combinatorial optimization to the continuous space of nonlinear optimization through geometric, analytic, and algebraic techniques. Many researchers have found that such approaches lead to very fast and efficient heuristics for solving large problems. Although almost all such heuristics work well in practice there is no solid theoretical analysis, except Karmakar's algorithm for linear programming. With this situation in mind, we decided to teach a seminar on nonlinear optimization with emphasis on its mathematical foundations. This book is the result of that seminar. During the last decades many textbooks and monographs in nonlinear optimization have been published. Why should we write this new one What is the difference of this book from the others The motivation for writing this book originated from our efforts to select a textbook for a graduate seminar with focus on the mathematical foundations of optimization. Codice articolo 9781441952028
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