Best Reference Books – Advanced Topics in Discrete Optimization

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We have compiled the list of Top 10 Best Reference Books on Advanced Topics In Discrete Optimization subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Advanced Topics In Discrete Optimization along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Advanced Topics In Discrete Optimization subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Advanced Topics In Discrete Optimization" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

1. “Geometric Algorithms and Combinatorial Optimization” by M. Gr ̈tschel

Book Review: This book demonstrates the theory of linear and integer programming and also demonstrates the algorithms thereby focusing on the complexity analysis. The book also covers recent developments in the field of linear and integer programming. This book is suitable for graduate students and researchers in the field of operations research, mathematics and computer science. The book contains chapters on linear algebra and its complexity, lattice theory and Diophantine equations and their algorithms, polyhedral structure, polarity, blocking and many more.

2. “Selected Topics on Continuous-Time Controlled Markov Chains and Markov Games” by Tomas Prieto-Rumeau

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“Selected Topics on Continuous-Time Controlled Markov Chains and Markov Games” Book Review: The book covers continuous-time controlled Markov chains and Markov games. The applications of both control and game models in economics, operations research, engineering, and computer science are mentioned in this book. Many features of the control and game models namely, the continuous time variable, the denumerable state space, the control sets, and Borel spaces are described in this book. Characterizing the optimal reward functions and determining optimal policies for each of the optimality criteria for controlled Markov chains and Markov games are thoroughly explained. Many advanced optimality criteria such as bias, variance, sensitive discount, and Blackwell optimality are covered in this text. The book features various exercises, problems, and their solutions.

3. “Geometry of Numbers” by C Lekkerkerker and P Gruber

Book Review: This book includes the geometry of numbers along with the relations to other branches of mathematics like analytic number theory, Diophantine approximation, coding and numerical analysis. The book also deals with the convex and non-convex bodies and lattices that are present in Euclidean space. The book also contains newer chapters on the recent developments made in the field of geometry of numbers. The book also demonstrates the progress made in the areas of geometry of numbers and the expected results.

4. “Optimization Over Integers” by D Bertsimas and R Weismantel

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Book Review: This book provides a unified treatment in the field of theory of integer optimization. The book is divided into four parts and they are formulations and relaxations, algebra and geometry of integer optimization, integer optimization algorithms and extensions of integer optimizations. The book illustrates the development of integer optimization theory via integral generating sets. The book also focuses on strong formulations, duality and relaxations. The book also discusses applications of lattices and algebraic geometry to integer optimization. The book also covers many enumerative and heuristic methods along with large number of examples and exercises.

5. “Algebraic and Geometric Ideas in the Theory of Discrete Optimization” by J De Loera and M K ̈ppe

Book Review: The book covers all the latest advancements in the field of mathematical theory of discrete optimization especially the methods from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions and many other optimization tools. The book also provides many research technologies and offers many techniques for learning these methods and also provides a transition from linear discrete optimization to nonlinear discrete optimization. The book is suitable for advanced graduate students in the field of mathematics, computer science and operations research.

6. “Discrete Optimization: The State of the Art” by Boros Endre

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“Discrete Optimization: The State of the Art” Book Review: The book is a comprehensive piece of writing featuring theoretical, computational and applied aspects of discrete optimization. It covers the tremendous progress in the preceding field in the last twenty years. The topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, applications to graph theory, mechanics, and chip design are discussed in this book. It also features some modern surveys written by the most prominent researchers in the field of discrete optimization.

7. “Discrete Optimization” by G L Nemhauser

“Discrete Optimization” Book Review: The book describes the latest methodological operations developments in transportation. The chapters of this book are well structured and cover topics like transport, its relationship with operations and management science, main transportation modes-air travel, automobile, public transit, and maritime transport. The recent research developments and theoretical and algorithmic developments in transportation are highlighted in this book. It contains an article based on the early history of discrete optimization. This book will be useful for the researchers, students, and practitioners related to the field of transportation.

8. “Progress in Combinatorial Optimization” by A Ridha Mahjoub

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“Progress in Combinatorial Optimization” Book Review: The book is updated and revised text presenting the latest developments and new trends in combinatorial optimization. The applications of combinatorial optimization in fields like communications, network design, VLSI, scheduling, production, and computational biology are highlighted in this book. The latest theory, concepts, results, and advances in areas such as computational complexity, approximation algorithms, cutting-plane based methods, and submodularity function minimization are described in this book. The book introduces more efficient and powerful methods for solving real-world problems.

9. “Ordinal Optimization” by Jia Zhao Ho

“Ordinal Optimization” Book Review: The book introduces simulation models and computation-intensive models for addressing the difficulties of the optimization of complex systems. It gives stochastic effects and discrete choices for problem solving. The advantages of the “softer” ordinal approach for search-based type problems are mentioned in this book. The general properties of ordinal approach and orders of magnitude improvement in computational efficiency are included. The book is basically for engineers and designers dealing with complex problems of optimization.

10. “Combinatorial Optimization : Theory And Algorithms” by Jens Vygen and Bernhard Korte

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“Combinatorial Optimization: Theory And Algorithms” Book Review: The book covers all the important topics related to Combinatorial Optimization. It consists of detailed theory, major techniques, algorithms, concise proofs, and many deep results of the featured topics. A chapter based on facility location problems is added in the book. Latest exercises and some new topics like linear programming, network simplex algorithm, and the max-cut problem are included in this book. The book will be a great reference for the researchers, practitioners, and students interested in combinatorial optimization.

People who are searching for Free downloads of books and free pdf copies of these top 10 books on Advanced Topics In Discrete Optimization – we would like to mention that we don’t have free downloadable pdf copies of these good books and one should look for free pdf copies from these Authors only if they have explicitly made it free to download and read them.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter