Advances In Applied Mathematics And Global Optimization
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Advances In Applied Mathematics And Global Optimization
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Author : David Y. Gao
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-09
Advances In Applied Mathematics And Global Optimization written by David Y. Gao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-09 with Mathematics categories.
The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and quantum computations, this collection reveals the beauty of these mathematical disciplines and investigates recent developments in global optimization, nonconvex and nonsmooth analysis, nonlinear programming, theoretical and engineering mechanics, large scale computation, quantum algorithms and computation, and information theory.
Combinatorial And Global Optimization
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Author : Rainer E Burkard
language : en
Publisher: World Scientific
Release Date : 2002-04-05
Combinatorial And Global Optimization written by Rainer E Burkard and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-05 with Mathematics categories.
Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, biological science, and computer science. In combinatorial optimization and graph theory, many approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. Recent major successes based on these approaches include interior point algorithms for linear and discrete problems, the celebrated Goemans-Williamson relaxation of the maximum cut problem, and the Du-Hwang solution of the Gilbert-Pollak conjecture. Since integer constraints are equivalent to nonconvex constraints, the fundamental difference between classes of optimization problems is not between discrete and continuous problems but between convex and nonconvex optimization problems. This volume is a selection of refereed papers based on talks presented at a conference on “Combinatorial and Global Optimization” held at Crete, Greece.
Convex Analysis And Global Optimization
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Author : Hoang Tuy
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Convex Analysis And Global Optimization written by Hoang Tuy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development. Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization.
Global Optimization
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Author : Marco Locatelli
language : en
Publisher: SIAM
Release Date : 2013-10-16
Global Optimization written by Marco Locatelli and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-16 with Mathematics categories.
This volume contains a thorough overview of the rapidly growing field of global optimization, with chapters on key topics such as complexity, heuristic methods, derivation of lower bounds for minimization problems, and branch-and-bound methods and convergence. The final chapter offers both benchmark test problems and applications of global optimization, such as finding the conformation of a molecule or planning an optimal trajectory for interplanetary space travel. An appendix provides fundamental information on convex and concave functions. Intended for Ph.D. students, researchers, and practitioners looking for advanced solution methods to difficult optimization problems. It can be used as a supplementary text in an advanced graduate-level seminar.
Advances In Convex Analysis And Global Optimization
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Author : Constantin Carathéodory
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-30
Advances In Convex Analysis And Global Optimization written by Constantin Carathéodory and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-30 with Computers categories.
There has been much recent progress in global optimization algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fundamental role in the analysis and development of global optimization algorithms. This is due to the fact that virtually all nonconvex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held June 5-9, 2000 at Pythagorian, Samos, Greece. It was in honor of the memory of C. Caratheodory (1873-1950). It was endorsed by the Mathematical Programming Society (MPS) and by the Society for industrial and Applied Mathematics (SIAN) Activity Group in Optimization. This volume contains a selection of refereed papers based on invited and contributing talks presented at the conference. The two themes of convexity and global optimization pervade the book. The conference provided a forum for researchers working on different aspects of convexity and global optimization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming. Audience: Faculty, graduate students, and researchers in mathematical programming, computer science, and engineering.
Advances And Trends In Optimization With Engineering Applications
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Author : Tamas Terlaky
language : en
Publisher: SIAM
Release Date : 2017-04-26
Advances And Trends In Optimization With Engineering Applications written by Tamas Terlaky and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-26 with Mathematics categories.
Optimization is of critical importance in engineering. Engineers constantly strive for the best possible solutions, the most economical use of limited resources, and the greatest efficiency. As system complexity increases, these goals mandate the use of state-of-the-art optimization techniques. In recent years, the theory and methodology of optimization have seen revolutionary improvements. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs. This is a two-way process: engineers benefit from developments in optimization methodology, and challenging new classes of optimization problems arise from novel engineering applications. Advances and Trends in Optimization with Engineering Applications reviews 10 major areas of optimization and related engineering applications, providing a broad summary of state-of-the-art optimization techniques most important to engineering practice. Each part provides a clear overview of a specific area and discusses a range of real-world problems. The book provides a solid foundation for engineers and mathematical optimizers alike who want to understand the importance of optimization methods to engineering and the capabilities of these methods.
Canonical Duality Theory
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Author : David Yang Gao
language : en
Publisher: Springer
Release Date : 2017-10-09
Canonical Duality Theory written by David Yang Gao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-09 with Mathematics categories.
This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.
Global Optimization Using Interval Analysis
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Author : Eldon Hansen
language : en
Publisher: CRC Press
Release Date : 2003-12-19
Global Optimization Using Interval Analysis written by Eldon Hansen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-19 with Mathematics categories.
Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.
Stochastic Global Optimization
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Author : Gade Pandu Rangaiah
language : en
Publisher: World Scientific
Release Date : 2010
Stochastic Global Optimization written by Gade Pandu Rangaiah and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
Ch. 1. Introduction / Gade Pandu Rangaiah -- ch. 2. Formulation and illustration of Luus-Jaakola optimization procedure / Rein Luus -- ch. 3. Adaptive random search and simulated annealing optimizers : algorithms and application issues / Jacek M. Jezowski, Grzegorz Poplewski and Roman Bochenek -- ch. 4. Genetic algorithms in process engineering : developments and implementation issues / Abdunnaser Younes, Ali Elkamel and Shawki Areibi -- ch. 5. Tabu search for global optimization of problems having continuous variables / Sim Mong Kai, Gade Pandu Rangaiah and Mekapati Srinivas -- ch. 6. Differential evolution : method, developments and chemical engineering applications / Chen Shaoqiang, Gade Pandu Rangaiah and Mekapati Srinivas -- ch. 7. Ant colony optimization : details of algorithms suitable for process engineering / V.K. Jayaraman [und weitere] -- ch. 8. Particle swarm optimization for solving NLP and MINLP in chemical engineering / Bassem Jarboui [und weitere] -- ch. 9. An introduction to the harmony search algorithm / Gordon Ingram and Tonghua Zhang -- ch. 10. Meta-heuristics : evaluation and reporting techniques / Abdunnaser Younes, Ali Elkamel and Shawki Areibi -- ch. 11. A hybrid approach for constraint handling in MINLP optimization using stochastic algorithms / G.A. Durand [und weitere] -- ch. 12. Application of Luus-Jaakola optimization procedure to model reduction, parameter estimation and optimal control / Rein Luus -- ch. 13. Phase stability and equilibrium calculations in reactive systems using differential evolution and tabu search / Adrian Bonilla-Petriciolet [und weitere] -- ch. 14. Differential evolution with tabu list for global optimization : evaluation of two versions on benchmark and phase stability problems / Mekapati Srinivas and Gade Pandu Rangaiah -- ch. 15. Application of adaptive random search optimization for solving industrial water allocation problem / Grzegorz Poplewski and Jacek M. Jezowski -- ch. 16. Genetic algorithms formulation for retrofitting heat exchanger network / Roman Bochenek and Jacek M. Jezowski -- ch. 17. Ant colony optimization for classification and feature selection / V.K. Jayaraman [und weitere] -- ch. 18. Constraint programming and genetic algorithm / Prakash R. Kotecha, Mani Bhushan and Ravindra D. Gudi -- ch. 19. Schemes and implementations of parallel stochastic optimization algorithms application of tabu search to chemical engineering problems / B. Lin and D.C. Miller