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Soft cover. Condición: New. Estado de la sobrecubierta: New. International Edition. **International edition** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service.…

Hardcover. Condición: New. Estado de la sobrecubierta: New. 1st Edition. **International edition** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service.…

Hardcover. Condición: New in new dust jacket. First edition. ***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. Trade paperback (US). 648 p. Die Grundlehren Der Mathematischen Wissenschaften., 315. Audience: Professional and scholarly.…

Hardcover. Condición: New in new dust jacket. First edition. ***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. Sewn binding. Cloth over boards. 618 p. Contains: Illustrations. NATO Asi Series, 315. Audience: General/trade.…

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Karton Karton. Condición: Sehr gut. 618, Seiten mit Abbildungen, Zust: Gutes Exemplar. Schneller Versand und persönlicher Service - jedes Buch händisch geprüft und beschrieben - aus unserem Familienbetrieb seit über 25 Jahren. Eine Rechnung mit ausgewiesener Mehrwertsteuer liegt jeder unserer Lieferungen bei. Wir versenden mit der deutschen Post. Sprache: Englisch Gewicht in Gramm: 1050.…

Paperback. Condición: New. The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro­ posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under­ standing of the intrinsic computational difficulty of problems. Softcover reprint of hardcover 1st ed. 1997.…

Condición: New. pp. 648.

Condición: gut. 1996. Algebraic Complexity Theory: With the Collab. of Thomas Lickteig (Grundlehren der mathematischen Wissenschaften, 315, Band 315) In deutscher Sprache. pages.

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Paperback. Condición: New. The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro­ posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under­ standing of the intrinsic computational difficulty of problems. Softcover reprint of hardcover 1st ed. 1997.…

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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Semidefinite Optimization has attracted the attention of many researchers over the last twenty years. It has nowadays a huge variety of applications in such different fields as Control, Structural Design, Statistics, or in the relaxation of hard combinatorial problems. In this thesis, we focus on the practical tractability of large-scale semidefinite optimization problems. From a theoretical point of view, these problems can be solved by polynomial-time Interior-Point methods approximately. The complexity estimate of Interior-Point methods grows logarithmically in the inverse of the solution accuracy, but with the order 3.5 in both the matrix size and the number of constraints. The later property prohibits the resolution of large-scale problems in practice.In this thesis, we present new approaches based on advanced First-Order methods such as Smoothing Techniques and Mirror-Prox algorithms for solving structured large-scale semidefinite optimization problems up to a moderate accuracy. These methods require a very specific problem format. However, generic semidefinite optimization problems do not comply with these requirements. In a preliminary step, we recast slightly structured semidefinite optimization problems in an alternative form to which these methods are applicable, namely as matrix saddle-point problems. The final methods have a complexity result that depends linearly in both the number of constraints and the inverse of the target accuracy.Smoothing Techniques constitute a two-stage procedure: we derive a smooth approximation of the objective function at first and apply an optimal First-Order method to the adapted problem afterwards. We present a refined version of this optimal First-Order method in this thesis. The worst-case complexity result for this modified scheme is of the same order as for the original method. However, numerical results show that this alternative scheme needs much less iterations than its original counterpart to find an approximate solution in practice. Using this refined version of the optimal First-Order method in Smoothing Techniques, we are able to solve randomly generated matrix saddle-point problems involving a hundred matrices of size 12'800 x 12'800 up to an absolute accuracy of 0.0012 in about four hours.Smoothing Techniques and Mirror-Prox methods require the computation of one or two matrix exponentials at every iteration when applied to the matrix saddle-point problems obtained from the above transformation step. Using standard techniques, the efficiency estimate for the exponentiation of a symmetric matrix grows cubically in the size of the matrix. Clearly, this operation limits the class of problems that can be solved by Smoothing Techniques and Mirror-Prox methods in practice. We present a randomized Mirror-Prox method where we replace the exact matrix exponential by a stochastic approximation. This randomized method outperforms all its competitors with respect to the theoretical complexity estimate on a significant class of large-scale matrix saddle-point problems. Furthermore, we show numerical results where the randomized method needs only about 58% of the CPU time of the deterministic counterpart for solving approximately randomly generated matrix saddle-point problems with a hundred matrices of size 800 × 800.As a side result of this thesis, we show that the Hedge algorithm - a method that is heavily used in Theoretical Computer Science - can be interpreted as a Dual Averaging scheme. The embedding of the Hedge algorithm in the framework of Dual Averaging schemes allows us to derive three new versions of this algorithm. The efficiency guarantees of these modified Hedge algorithms are at least as good as, sometimes even better than, the complexity estimates of the original method. We present numerical experiments where the refined methods significantly outperform their vanilla counterpart. 204 pp. Englisch.…

Taschenbuch. Condición: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Semidefinite Optimization has attracted the attention of many researchers over the last twenty years. It has nowadays a huge variety of applications in such different fields as Control, Structural Design, Statistics, or in the relaxation of hard combinatorial problems. In this thesis, we focus on the practical tractability of large-scale semidefinite optimization problems. From a theoretical point of view, these problems can be solved by polynomial-time Interior-Point methods approximately. The complexity estimate of Interior-Point methods grows logarithmically in the inverse of the solution accuracy, but with the order 3.5 in both the matrix size and the number of constraints. The later property prohibits the resolution of large-scale problems in practice.In this thesis, we present new approaches based on advanced First-Order methods such as Smoothing Techniques and Mirror-Prox algorithms for solving structured large-scale semidefinite optimization problems up to a moderate accuracy. These methods require a very specific problem format. However, generic semidefinite optimization problems do not comply with these requirements. In a preliminary step, we recast slightly structured semidefinite optimization problems in an alternative form to which these methods are applicable, namely as matrix saddle-point problems. The final methods have a complexity result that depends linearly in both the number of constraints and the inverse of the target accuracy.Smoothing Techniques constitute a two-stage procedure: we derive a smooth approximation of the objective function at first and apply an optimal First-Order method to the adapted problem afterwards. We present a refined version of this optimal First-Order method in this thesis. The worst-case complexity result for this modified scheme is of the same order as for the original method. However, numerical results show that this alternative scheme needs much less iterations than its original counterpart to find an approximate solution in practice. Using this refined version of the optimal First-Order method in Smoothing Techniques, we are able to solve randomly generated matrix saddle-point problems involving a hundred matrices of size 12¿800 x 12¿800 up to an absolute accuracy of 0.0012 in about four hours.Smoothing Techniques and Mirror-Prox methods require the computation of one or two matrix exponentials at every iteration when applied to the matrix saddle-point problems obtained from the above transformation step. Using standard techniques, the efficiency estimate for the exponentiation of a symmetric matrix grows cubically in the size of the matrix. Clearly, this operation limits the class of problems that can be solved by Smoothing Techniques and Mirror-Prox methods in practice. We present a randomized Mirror-Prox method where we replace the exact matrix exponential by a stochastic approximation. This randomized method outperforms all its competitors with respect to the theoretical complexity estimate on a significant class of large-scale matrix saddle-point problems. Furthermore, we show numerical results where the randomized method needs only about 58% of the CPU time of the deterministic counterpart for solving approximately randomly generated matrix saddle-point problems with a hundred matrices of size 800 × 800.As a side result of this thesis, we show that the Hedge algorithm ¿ a method that is heavily used in Theoretical Computer Science ¿ can be interpreted as a Dual Averaging scheme. The embedding of the Hedge algorithm in the framework of Dual Averaging schemes allows us to derive three new versions of this algorithm. The efficiency guarantees of these modified Hedge algorithms are at least as good as, sometimes even better than, the complexity estimates of the original method. We present numerical experiments where the refined methods significantly outperform their vanilla counterpart. …