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Integer Programming
A PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED The revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems.The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared.The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers.The result has been a speed-up of several orders of magnitude.The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders’ decomposition.The revised second edition: Contains new developments on column generationOffers a new chapter on Benders’ algorithmIncludes expanded information on preprocessing, heuristics, and branch-and-cutPresents several basic and extended formulations, for example for fixed costnetwork flowsAlso touches on and briefly introduces topics such as non-bipartite matching, the complexity of extended formulations or a good linear program for the implementation of lift-and-project Written for students of integer/mathematical programming in operations research, mathematics, engineering, or computer science, Integer Programming offers an updated edition of the basic text that reflects the most recent developments in the field.
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Integer Algorithms In Cryptology And Information Assurance
Integer Algorithms in Cryptology and Information Assurance is a collection of the author's own innovative approaches in algorithms and protocols for secret and reliable communication.It concentrates on the "what" and "how" behind implementing the proposed cryptographic algorithms rather than on formal proofs of "why" these algorithms work.The book consists of five parts (in 28 chapters) and describes the author's research results in:This text contains innovative cryptographic algorithms; computationally efficient algorithms for information assurance; new methods to solve the classical problem of integer factorization, which plays a key role in cryptanalysis; and numerous illustrative examples and tables that facilitate the understanding of the proposed algorithms.The fundamental ideas contained within are not based on temporary advances in technology, which might become obsolete in several years.The problems addressed in the book have their own intrinsic computational complexities, and the ideas and methods described in the book will remain important for years to come.
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Linear and Integer Optimization : Theory and Practice, Third Edition
Presenting a strong and clear relationship between theory and practice, Linear and Integer Optimization: Theory and Practice is divided into two main parts.The first covers the theory of linear and integer optimization, including both basic and advanced topics.Dantzig’s simplex algorithm, duality, sensitivity analysis, integer optimization models, and network models are introduced.More advanced topics also are presented including interior point algorithms, the branch-and-bound algorithm, cutting planes, complexity, standard combinatorial optimization models, the assignment problem, minimum cost flow, and the maximum flow/minimum cut theorem. The second part applies theory through real-world case studies.The authors discuss advanced techniques such as column generation, multiobjective optimization, dynamic optimization, machine learning (support vector machines), combinatorial optimization, approximation algorithms, and game theory. Besides the fresh new layout and completely redesigned figures, this new edition incorporates modern examples and applications of linear optimization.The book now includes computer code in the form of models in the GNU Mathematical Programming Language (GMPL).The models and corresponding data files are available for download and can be readily solved using the provided online solver. This new edition also contains appendices covering mathematical proofs, linear algebra, graph theory, convexity, and nonlinear optimization.All chapters contain extensive examples and exercises.This textbook is ideal for courses for advanced undergraduate and graduate students in various fields including mathematics, computer science, industrial engineering, operations research, and management science.
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Museums and Interactive Virtual Learning
Museums and Interactive Virtual Learning provides informal educators with practical resources that will help them to build dynamic digital engagement experiences within their own cultural organizations. Presenting vignettes from experienced museum educators and end users, as well as scientific data and practical resources, the book highlights the mutual benefits that Interactive Virtual Learning (IVL) programs offer to the museum and those visiting from a distance.Chapters mirror the step-by-step process of developing reputable IVL programs and emphasize how important it is for cultural organizations to encourage cross-departmental collaboration, if they wish to ensure that their programs align with the overall goals of the organization.Providing a thorough overview of the technologies, budget, marketing and staff requirements, the authors offer a realistic depiction of the work involved in building content for digital engagement.Emphasizing the importance of assessing existing programming, the book shows how institutions can adapt content to fit a virtual format and create inclusive digital engagement opportunities that reach local, national, and international audiences. Museums and Interactive Virtual Learning is an essential guide for professionals who are tasked with interpreting the content of a cultural organization and building lasting digital engagement opportunities.It will be particularly useful to those looking to reach diverse audiences.
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Marco De Bartoli - Integer zibibbo 2022 | White Wine | 75cL | Italy
1 x 75cl. From Zibibbo grapes comes the Integer Zibibbo Terre Siciliane IGT wine, a label with a characteristic and balanced taste with the signature of Marco De Bartoli. The result of a process aimed at achieving high quality levels, it is produced in the area of Pantelleria (TP). The Integer Zibibbo wine reveals nuances of taste capable of delighting the palate in the company of appetizers and first courses of fish or vegetables.
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Marco De Bartoli - Integer grillo 2021 | White Wine | 75cL | Italy
1 x 75cl. Integer Grillo is a Terre Siciliane IGT white wine by Marco De Bartoli. This label is the result of a winemaking process dedicated to genuineness and passion, which begins between the rows of Grillo, in the area of Marsala (TP), and ends in the bottle. Its properties are evidence of this, which, on the whole, make it an elegant and lively wine, ideal to accompany appetizers and first courses of fish or vegetables.
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Around the Unit Circle : Mahler Measure, Integer Matrices and Roots of Unity
Mahler measure, a height function for polynomials, is the central theme of this book.It has many interesting properties, obtained by algebraic, analytic and combinatorial methods.It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981).This book contains a wide range of results on Mahler measure.Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture.Other known results are included with new, streamlined proofs.Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book.One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices.In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work.Many Mahler measure results are proved for restricted setsof polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices.For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way.Numerous exercises at various levels are given, including some for computer programming.A wide range of stimulating open problems is also included.At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour.It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure.Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.
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Mathematical Programming Approaches for Multi-Vehicle Motion Planning : Linear, Nonlinear, and Mixed Integer Programming
Real world Multi-Vehicle Motion Planning (MVMP) problems require the optimization of suitable performance measures under an array of complex and challenging constraints involving kinematics, dynamics, collision avoidance, and communication connectivity.The general MVMP problem is thus formulated as a Mathematical Programming (Optimization) problem. This book presents a Mathematical Programming (MP) framework that captures the salient features of the general MVMP problem.To demonstrate the use of MP for the formulation and solution of MVMP problems, it examines in detail four representative works and summarizes several other related ones.Following this conceptual discussion, it provides a step-by-step demonstration of how to formulate, solve, and experimentally validate an MP problem that represents a MVMP.Finally, it discusses the advantages, technical challenges, and limitations of this framework. As solution algorithms and their implementations in solvers continue to develop, it is anticipated that MP solution techniques will be applied to an increasing number of MVMP problems.The framework, formulations, and experimental approach presented here may serve as a guide for future MVMP research.
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