Numerical Infinities And Infinitesimals In Optimization

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Numerical Infinities and Infinitesimals in Optimization

Author : Yaroslav D. Sergeyev
Publisher : Springer Nature
ISBN 13 : 3030936422
Total Pages : 372 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Numerical Infinities and Infinitesimals in Optimization by : Yaroslav D. Sergeyev

Download or read book Numerical Infinities and Infinitesimals in Optimization written by Yaroslav D. Sergeyev and published by Springer Nature. This book was released on 2022-07-05 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science. “Mathematicians have never been comfortable handling infinities... But an entirely new type of mathematics looks set to by-pass the problem... Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem... ” MIT Technology Review “These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used.” A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing. “I am sure that the new approach ... will have a very deep impact both on Mathematics and Computer Science.” D. Trigiante, Computational Management Science. “Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural”. R. Gangle, G. Caterina, F. Tohmé, Soft Computing. “The computational features offered by the Infinity Computer allow us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort.” P. Amodio, L. Brugnano, F. Iavernaro & F. Mazzia, Soft Computing

Numerical Infinities and Infinitesimals in Optimization

Author : Yaroslav D. Sergeyev
Publisher :
ISBN 13 : 9788303093646
Total Pages : 0 pages
Book Rating : 4.0/5 (936 download)

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Book Synopsis Numerical Infinities and Infinitesimals in Optimization by : Yaroslav D. Sergeyev

Download or read book Numerical Infinities and Infinitesimals in Optimization written by Yaroslav D. Sergeyev and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science.

Mathematical Optimization Theory and Operations Research

Author : Michael Khachay
Publisher : Springer Nature
ISBN 13 : 3031353056
Total Pages : 459 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Mathematical Optimization Theory and Operations Research by : Michael Khachay

Download or read book Mathematical Optimization Theory and Operations Research written by Michael Khachay and published by Springer Nature. This book was released on 2023-06-25 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 22nd International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2023, held in Ekaterinburg, Russia, during July 2–8, 2023. The 28 full papers and 1 short paper included in this book were carefully reviewed and selected from 89 submissions. They were organized in topical sections as follows: Mathematical programming and applications; discrete and combinatorial optimization; stochastic optimization; scheduling; game theory; and optimal control and mathematical economics. The book also contains one invited talk in full paper length.

Mathematical Optimization Theory and Operations Research

Author : Panos Pardalos
Publisher : Springer Nature
ISBN 13 : 303109607X
Total Pages : 332 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Mathematical Optimization Theory and Operations Research by : Panos Pardalos

Download or read book Mathematical Optimization Theory and Operations Research written by Panos Pardalos and published by Springer Nature. This book was released on 2022-06-24 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 21st International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2022, held in Petrozavodsk, Russia, in July 2022. The 21 full papers presented together with 6 invited abstracts lectures and 2 tutorial abstracts in this volume were carefully reviewed and selected from 88 submissions. The conference focuses on the following topics: Mathematical programming, bi-level and global optimization, integer programming and combinatorial optimization, approximation algorithms with theoretical guarantees and approximation schemes, heuristics and meta-heuristics, game theory, optimal control, optimization in machine learning and data analysis, and their valuable applications in operations research and economics.

Learning and Intelligent Optimization

Author : Dimitris E. Simos
Publisher : Springer Nature
ISBN 13 : 303124866X
Total Pages : 576 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Learning and Intelligent Optimization by : Dimitris E. Simos

Download or read book Learning and Intelligent Optimization written by Dimitris E. Simos and published by Springer Nature. This book was released on 2023-02-04 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 16th International Conference on Learning and Intelligent Optimization, LION 16, which took place in Milos Island, Greece, in June 2022. The 36 full papers and 3 short papers presented in this volume were carefully reviewed and selected from 60 submissions. LION deals with automatic solver configuration, parallel methods, intelligent optimization, nature-inspired algorithms, hard combinatorial optimization problems, DC learning, computational intelligence, and others. The contributions were organized in topical sections as follows: Invited Papers; Contributed Papers.

Numerical Computations: Theory and Algorithms

Author : Yaroslav D. Sergeyev
Publisher : Springer Nature
ISBN 13 : 3030406164
Total Pages : 550 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Numerical Computations: Theory and Algorithms by : Yaroslav D. Sergeyev

Download or read book Numerical Computations: Theory and Algorithms written by Yaroslav D. Sergeyev and published by Springer Nature. This book was released on 2020-02-13 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 11973 and 11974 constitute revised selected papers from the Third International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2019, held in Crotone, Italy, in June 2019. This volume, LNCS 11974, consists of 19 full and 32 short papers chosen among regular papers presented at the the Conference including also the paper of the winner (Lorenzo Fiaschi, Pisa, Italy) of The Springer Young Researcher Prize for the best NUMTA 2019 presentation made by a young scientist. The papers in part II explore the advanced research developments in such interconnected fields as local and global optimization, machine learning, approximation, and differential equations. A special focus is given to advanced ideas related to methods and applications using emerging computational paradigms.

Learning and Intelligent Optimization

Author : Roberto Battiti
Publisher : Springer
ISBN 13 : 3030053482
Total Pages : 487 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Learning and Intelligent Optimization by : Roberto Battiti

Download or read book Learning and Intelligent Optimization written by Roberto Battiti and published by Springer. This book was released on 2018-12-31 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 12th International Conference on Learning and Intelligent Optimization, LION 12, held in Kalamata, Greece, in June 2018. The 28 full papers and 12 short papers presented have been carefully reviewed and selected from 62 submissions. The papers explore the advanced research developments in such interconnected fields as mathematical programming, global optimization, machine learning, and artificial intelligence. Special focus is given to advanced ideas, technologies, methods, and applications in optimization and machine learning.

Numerical Optimization

Author : Joseph-Frédéric Bonnans
Publisher : Springer Science & Business Media
ISBN 13 : 3662050781
Total Pages : 421 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Numerical Optimization by : Joseph-Frédéric Bonnans

Download or read book Numerical Optimization written by Joseph-Frédéric Bonnans and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical description when coming to actual implementation.

Numerical Optimization

Author : Jorge Nocedal
Publisher : Springer Science & Business Media
ISBN 13 : 0387227423
Total Pages : 651 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Numerical Optimization by : Jorge Nocedal

Download or read book Numerical Optimization written by Jorge Nocedal and published by Springer Science & Business Media. This book was released on 2006-06-06 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this book presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on methods best suited to practical problems. This edition has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are widely used in practice and are the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience.

Large-scale Numerical Optimization

Author : Thomas Frederick Coleman
Publisher : SIAM
ISBN 13 : 9780898712681
Total Pages : 278 pages
Book Rating : 4.7/5 (126 download)

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Book Synopsis Large-scale Numerical Optimization by : Thomas Frederick Coleman

Download or read book Large-scale Numerical Optimization written by Thomas Frederick Coleman and published by SIAM. This book was released on 1990-01-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from a workshop held at Cornell University, Oct. 1989, and sponsored by Cornell's Mathematical Sciences Institute. Annotation copyright Book News, Inc. Portland, Or.

Bayesian and High-Dimensional Global Optimization

Author : Anatoly Zhigljavsky
Publisher : Springer Nature
ISBN 13 : 3030647129
Total Pages : 125 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Bayesian and High-Dimensional Global Optimization by : Anatoly Zhigljavsky

Download or read book Bayesian and High-Dimensional Global Optimization written by Anatoly Zhigljavsky and published by Springer Nature. This book was released on 2021-03-02 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible to a variety of readers, this book is of interest to specialists, graduate students and researchers in mathematics, optimization, computer science, operations research, management science, engineering and other applied areas interested in solving optimization problems. Basic principles, potential and boundaries of applicability of stochastic global optimization techniques are examined in this book. A variety of issues that face specialists in global optimization are explored, such as multidimensional spaces which are frequently ignored by researchers. The importance of precise interpretation of the mathematical results in assessments of optimization methods is demonstrated through examples of convergence in probability of random search. Methodological issues concerning construction and applicability of stochastic global optimization methods are discussed, including the one-step optimal average improvement method based on a statistical model of the objective function. A significant portion of this book is devoted to an analysis of high-dimensional global optimization problems and the so-called ‘curse of dimensionality’. An examination of the three different classes of high-dimensional optimization problems, the geometry of high-dimensional balls and cubes, very slow convergence of global random search algorithms in large-dimensional problems , and poor uniformity of the uniformly distributed sequences of points are included in this book.

Arithmetic of infinity

Author : Yaroslav D. Sergeyev
Publisher : Yaroslav D. Sergeyev
ISBN 13 : 8889064013
Total Pages : 112 pages
Book Rating : 4.8/5 (89 download)

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Book Synopsis Arithmetic of infinity by : Yaroslav D. Sergeyev

Download or read book Arithmetic of infinity written by Yaroslav D. Sergeyev and published by Yaroslav D. Sergeyev. This book was released on 2016-05-13 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first chapter of the book gives a brief description of the modern viewpoint on real numbers and presents the famous results of Georg Cantor regarding infinity. The second chapter has a preparative character and links the first and the third parts of the book. On the one hand, it shows that the commonly accepted point of view on numbers and infinity is not so clear as it seems at first sight (for example, it leads to numerous paradoxes). On the other hand, the chapter contains preliminary observations that will be used in the constructive introduction of a new arithmetic of infinity, given in the third chapter. This last part of the book contains the main results. It introduces notions of infinite and infinitesimal numbers, extended natural and real numbers, and operations with them. Surprisingly, the introduced arithmetical operations result in being very simple and are obtained as immediate extensions of the usual addition, multiplication, and division of finite numbers to infinite ones. This simplicity is a consequence of a newly developed positional numeral system used to express infinite numbers. Finally, the chapter contains solutions to a number of paradoxes regarding infinity (we can say that the new approach allows us to avoid paradoxes) and some examples of applications. In order to broaden the audience, the book was written as a popular one. The interested reader can find a number of technical articles of several researches that use the approach introduced here for solving a variety of research problems at the web page of the author. The author Yaroslav D. Sergeyev is Distinguished Professor and Head of Numerical Calculus Laboratory at the University of Calabria, Italy. He is also Professor (part-time contract) at Lobachevsky Nizhni Novgorod State University, Russia. His research interests include numerical analysis, global optimization, infinity computing, set theory, number theory, fractals, and parallel computing. He has been awarded several national and international prizes (Pythagoras International Prize in Mathematics, Italy; Lagrange Lecture, Turin University, Italy; MAIK Prize for the best scientific monograph published in Russian, Moscow, etc.). His list of scientific publications contains more than 200 items. He is a member of editorial boards of 5 international journals and has given more than 50 plenary and keynote lectures at prestigious international congresses.

Infinite-Dimensional Optimization and Convexity

Author : Ivar Ekeland
Publisher : University of Chicago Press
ISBN 13 : 0226199886
Total Pages : 175 pages
Book Rating : 4.2/5 (261 download)

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Book Synopsis Infinite-Dimensional Optimization and Convexity by : Ivar Ekeland

Download or read book Infinite-Dimensional Optimization and Convexity written by Ivar Ekeland and published by University of Chicago Press. This book was released on 1983-09-15 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The caratheodory approach; Infinite-dimensional optimization; Duality theory.

Evolutionary Multi-Criterion Optimization

Author : Hisao Ishibuchi
Publisher : Springer Nature
ISBN 13 : 3030720624
Total Pages : 781 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Evolutionary Multi-Criterion Optimization by : Hisao Ishibuchi

Download or read book Evolutionary Multi-Criterion Optimization written by Hisao Ishibuchi and published by Springer Nature. This book was released on 2021-03-24 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2021 held in Shenzhen, China, in March 2021. The 47 full papers and 14 short papers were carefully reviewed and selected from 120 submissions. The papers are divided into the following topical sections: theory; algorithms; dynamic multi-objective optimization; constrained multi-objective optimization; multi-modal optimization; many-objective optimization; performance evaluations and empirical studies; EMO and machine learning; surrogate modeling and expensive optimization; MCDM and interactive EMO; and applications.

Linear Semi-Infinite Optimization

Author : Miguel A. Goberna
Publisher :
ISBN 13 :
Total Pages : 380 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Linear Semi-Infinite Optimization by : Miguel A. Goberna

Download or read book Linear Semi-Infinite Optimization written by Miguel A. Goberna and published by . This book was released on 1998-03-11 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: A linear semi-infinite program is an optimization problem with linear objective functions and linear constraints in which either the number of unknowns or the number of constraints is finite. The many direct applications of linear semi-infinite optimization (or programming) have prompted considerable and increasing research effort in recent years. The authors' aim is to communicate the main theoretical ideas and applications techniques of this fascinating area, from the perspective of convex analysis. The four sections of the book cover: * Modelling with primal and dual problems - the primal problem, space of dual variables, the dual problem. * Linear semi-infinite systems - existence theorems, alternative theorems, redundancy phenomena, geometrical properties of the solution set. * Theory of linear semi-infinite programming - optimality, duality, boundedness, perturbations, well-posedness. * Methods of linear semi-infinite programming - an overview of the main numerical methods for primal and dual problems. Exercises and examples are provided to illustrate both theory and applications. The reader is assumed to be familiar with elementary calculus, linear algebra and general topology. An appendix on convex analysis is provided to ensure that the book is self-contained. Graduate students and researchers wishing to gain a deeper understanding of the main ideas behind the theory of linear optimization will find this book to be an essential text.

Learning and Intelligent Optimization

Author : Dimitris E. Simos
Publisher : Springer
ISBN 13 : 9783030921200
Total Pages : 410 pages
Book Rating : 4.9/5 (212 download)

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Book Synopsis Learning and Intelligent Optimization by : Dimitris E. Simos

Download or read book Learning and Intelligent Optimization written by Dimitris E. Simos and published by Springer. This book was released on 2021-12-09 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-conference proceedings on Learning and Intelligent Optimization, LION 15, held in Athens, Greece, in June 2021. The 30 full papers presented have been carefully reviewed and selected from 35 submissions. LION deals with designing and engineering ways of "learning" about the performance of different techniques, and ways of using past experience about the algorithm behavior to improve performance in the future. Intelligent learning schemes for mining the knowledge obtained online or offline can improve the algorithm design process and simplify the applications of high-performance optimization methods. Combinations of different algorithms can further improve the robustness and performance of the individual components.

Dynamics of Information Systems: Algorithmic Approaches

Author : Alexey Sorokin
Publisher : Springer Science & Business Media
ISBN 13 : 1461475821
Total Pages : 347 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Dynamics of Information Systems: Algorithmic Approaches by : Alexey Sorokin

Download or read book Dynamics of Information Systems: Algorithmic Approaches written by Alexey Sorokin and published by Springer Science & Business Media. This book was released on 2013-08-23 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamics of Information Systems: Algorithmic Approaches presents recent developments and results found by participants of the Fourth International Conference on the Dynamics of Information Systems, which took place at the University of Florida, Gainesville FL, USA on February 20-22, 2012. The purpose of this conference was to bring together scientists and engineers from industry, government, and universities to exchange knowledge and results in a broad range of topics relevant to the theory and practice of the dynamics of information systems.Dynamics of Information plays an increasingly critical role in our society. The influence of information on social, biological, genetic, and military systems must be better understood to achieve large advances in the capability and understanding of these systems. Applications are widespread and include: detection of terrorist networks, design of highly efficient businesses, computer networks, quantum entanglement, genome modeling, multi-robotic systems, and industrial and manufacturing safety. The book contains state-of-the-art work on theory and practice relevant to the dynamics of information systems. It covers algorithmic approaches to numerical computations with infinite and infinitesimal numbers; presents important problems arising in service-oriented systems, such as dynamic composition and analysis of modern service-oriented information systems and estimation of customer service times on a rail network from GPS data; addresses the complexity of the problems arising in stochastic and distributed systems; and discusses modulating communication for improving multi-agent learning convergence. Network issues—in particular minimum-risk maximum-clique problems, vulnerability of sensor networks, influence diffusion, community detection, and link prediction in social network analysis, as well as a comparative analysis of algorithms for transmission network expansion planning—are described in later chapters.