Level-Up Your Optimization Knowledge

At Gurobi, we’re passionate about mathematical optimization and training up the next generation of optimization professionals. So whether you’re a seasoned operations research professional, or you’re just getting started with mathematical optimization, this curated list has something for you. Be sure to also check out our free training resources, as well as our personalized training options.

Interesting Books

Model Building in Mathematical Programming

By H. Paul Williams

If you’ve ever wondered how to translate real-world problems into mathematical language, “Model Building in Mathematical Programming” is the book for you. This comprehensive guide takes you on a journey through the intricate landscape of mathematical optimization, breaking it down into four digestible parts.

  • The Basics: Learn the fundamentals of linear optimization models, illustrated with practical examples. Understand the nuances of objective functions and constraints, including discrete vs. continuous model components.
  • Problem Areas: This section is a goldmine for anyone looking to understand problem formulation from a mathematician’s perspective. It presents problems in a structured manner, often with hints for possible modeling approaches.
  • From Problems to Models: Witness the transformation of real-world problems into mathematical models. This section not only introduces you to different model variants but also guides you step-by-step to complex models, highlighting where integer programming is essential.
  • Solutions Unveiled: The book closes the loop by presenting solutions in a concise format, aligned with the original problem statements.

The book intentionally avoids discussing solution methods, focusing instead on the art of modeling. Ideal for advanced students and professionals, this book is a must-read for anyone serious about mastering mathematical modeling.


Introduction to Linear Optimization

By Dimitris Bertsimas and John N. Tsitsiklis

Introduction to Linear Optimization” is a well-crafted book that offers a deep dive into the subject, from foundational principles to advanced topics. Here’s why this book stands out:

  • Clarity and Depth: The book excels in presenting the foundations of linear programming in a clear yet rigorous manner. It supplements abstract mathematical concepts with intuitive geometrical explanations, making it easier to grasp complex ideas.
  • Comprehensive Coverage: From simplex methods to modern optimization techniques, the book covers a wide array of topics. It even delves into applications in network flows and integer programming, ensuring you have a well-rounded understanding of the field.
  • Critical Thinking: While the book is detailed, it challenges you to think critically. It often condenses complex steps into single sentences, prompting you to dig deeper and fully understand the material.
  • Real-world Applications: The book is not just theoretical; it provides practical insights into how to visualize problems and build algorithms for solving linear programs.
  • For All Levels: Whether you’re an advanced undergraduate, a graduate student, or a professional in the field, this book has something to offer. It’s considered one of the best textbooks for learning linear programming theory.

The book assumes a strong grasp of previous chapters when introducing new material, but if you’re up for the challenge, this book is an invaluable resource for mastering linear optimization.


Linear Programming: Foundations and Extensions

By Robert Vanderbei

Linear Programming: Foundations and Extensions” offers a balanced approach between theory and application, making it an ideal resource for both graduate students and professionals. Here’s what sets it apart:

  • Theoretical Depth: The book provides a thorough treatment of linear models, their properties, and duality theory. It doesn’t just tell you how to solve problems—it explains why the methods work.
  • Algorithmic Breadth: The author, a leading researcher in interior-point methods, presents a variety of algorithms, including the simplex method and interior-point methods. Each algorithm is demonstrated with examples and summarized in pseudocode, making it easier to implement.
  • Practical Insights: The book goes beyond theory to discuss implementation issues. If you’re looking to write your own code to solve real-world problems, this book offers invaluable guidance.
  • Extensions and Applications: The book covers integer programming, convex programming, network optimization, and even game theory. The newer editions also include problems in financial engineering, making it a timely resource.
  • Advanced Material: For those looking for a deeper dive, the book includes advanced topics like degeneracy and cycling in the simplex method, convexity analysis, and the homogeneous self-dual method. These are particularly useful for researchers and those in a Ph.D.-level course.
  • Balanced Approach: Unlike many other texts that focus either strictly on theory or solely on applications, this book strikes a delicate balance between the two. It effectively treats both the “why” and the “how,” making it a comprehensive guide to the subject.

Whether you’re a beginner looking to get more familiar with linear programming or an expert seeking to deepen your knowledge, this book is a valuable addition to your library.


Primal-Dual Interior Point Methods

by Stephen J. Wright

Some works stand the test of time—and Stephen Wright’s “Primal-Dual Interior-Point Methods,” published in 1987, is one such classic. Here’s why this enduring book remains relevant:

  • Comprehensive Coverage: The book presents the major primal-dual algorithms for linear programming in a straightforward manner. It covers path-following algorithms, potential-reduction algorithms, and infeasible-interior-point algorithms, offering a well-rounded view of the subject.
  • Theoretical Rigor: The book delves deep into the theoretical properties of these algorithms, providing a unified treatment of superlinear convergence, finite termination, and the detection of infeasible problems.
  • Practical Insights: Beyond theory, the book discusses practical and computational aspects, including sparse linear algebra and a complete specification of Mehrotra’s predictor-corrector algorithm. This makes it an invaluable resource for those looking to implement these algorithms.
  • Extensions and Variants: The book goes beyond linear programming to discuss extensions of primal-dual algorithms to more general problems like monotone complementarity, semidefinite programming, and general convex programming problems.
  • For All Levels: Whether you’re a student, a researcher, or a professional, this book offers something for everyone. Its clear exposition and thorough description make it accessible, yet it doesn’t shy away from the complexities of the subject.

If you’re interested in understanding the roots of primal-dual algorithms and interior-point methods, this timeless classic is an essential read.


Integer Programming

By Laurence A. Wolsey

Master the art of solving optimization problems with discrete or integer variables with Laurence A. Wolsey’s, “Integer Programming“:

  • Practical and Accessible: Unlike other textbooks that focus solely on theory, this book offers a practical, accessible guide to constructing custom-made algorithms or using existing commercial software to solve real-world problems.
  • Good vs. Bad Formulations: One of the standout features of this book is its focus on distinguishing between good and bad formulations in integer programming problems. This is invaluable for anyone looking to apply these techniques in practice.
  • Lessons from Easy to Difficult: The book applies lessons learned from solving easy integer programs to tackle more complex problems. This progressive approach makes it easier to grasp the intricacies of integer programming.
  • Comprehensive Exercises: Each chapter includes useful notes and end-of-chapter exercises that offer tremendous flexibility for tailoring the material to different needs.
  • Ideal for Multiple Disciplines: Whether you’re in operations research, mathematics, engineering, or computer science, this book is an ideal text for courses in integer or mathematical programming. It’s also a valuable reference for industrial users and researchers.
  • Theoretical and Practical Aspects: The book doesn’t just teach you how to solve problems; it also delves into the theoretical aspects, offering a well-rounded understanding of the subject.

If you’re serious about delving into the world of integer programming, this book offers a comprehensive, state-of-the-art guide that is both practical and theoretically sound. The second edition, published in 2020, covers new developments in column generation, Benders’ algorithm, expanded information on preprocessing, heuristics, branch-and-cut, and more.


Introduction to Operations Research

By Frederick Hillier and Gerald Lieberman

Are you intrigued by the idea of making better decisions—decisions that are more informed, more efficient, and more impactful? If so, “Introduction to Operations Research” by Frederick Hillier and Gerald Lieberman is the book you’ve been waiting for.

For over four decades, this book has been the go-to text for students and professionals alike in the field of operations research. It’s not just a book; it’s a treasure trove of state-of-the-art, user-friendly software and real-world business applications. The authors have continuously updated the content to make it current and relevant, ensuring that you’re not just learning theories but also how to apply them in today’s fast-paced world.

Two key features make this book a must-read.

  • First, it’s incredibly student-friendly, offering excellent motivation, clear and intuitive explanations, and practical examples from professional practice. The book is organized in a way that makes complex topics accessible, supported by software that enhances learning.
  • Second, instructors find the book invaluable for its ability to infuse state-of-the-art material with remarkable clarity. It strikes the perfect balance between academic rigor and practical application, making it a comprehensive guide for anyone looking to master the art of decision-making through operations research.

If you’re ready to elevate your decision-making skills and delve into the fascinating world of operations research, this book is your ultimate guide.


Puzzles and Games: A Mathematical Modeling Approach

By Tony Hürlimann

Puzzles and Games: A Mathematical Modeling Approach” explores about 100 puzzles as “case studies” and represents them as mathematical models. By dissecting the mechanics of each, it offers a unique blend of practical and theoretical understanding. Ideal for a wide audience—from mathematicians and engineers to game enthusiasts—the book is designed to be accessible to people with varying levels of mathematical background. Enjoy this topic? Check out our blog post, “Finding Mathematical Optimization in Unexpected Places: Games and Puzzles.”


Opt Art: From Mathematical Optimization to Visual Design

By Robert Bosch 

Opt Art: From Mathematical Optimization to Visual Design” by Robert Bosch is a captivating exploration of how mathematical optimization techniques can be harnessed to create stunning visual art. The book serves as a unique blend of a coffee table book’s artistic beauty and enriching classroom exposition. It’s not just a collection of beautiful images; it’s a comprehensive guide that teaches you the mathematics of optimization in an engaging and accessible manner. Bosch’s delight in teasing out the tensions between constraint and creativity is evident on every page. From Legos to dominoes and from mazes to the Mona Lisa, the book shows how simple linear equations can become a powerful tool in the hands of a mathematical artist. Enjoy this topic? Check out our blog post, “Finding Mathematical Optimization in Unexpected Places: The Art World.”


The Optimization Edge: Reinventing Decision Making to Maximize All Your Company’s Assets

By Steve Sashihara

The Optimization Edge: Reinventing Decision Making to Maximize All Your Company’s Assets” by Steve Sashihara offers a compelling guide to integrating optimization into the core business processes of your organization. Written by the CEO of Princeton Consultants Inc., a firm specializing in blending information technology and management consulting, this book is a treasure trove of insights for executives and innovators alike. It goes beyond buzzwords like “Big Data” to focus on “Big Optimization,” providing a maturity model to help companies assess their state of optimization and identify areas of opportunity. Whether you’re a seasoned executive or an emerging leader, this book equips you with the tools and frameworks to make better decisions, maximize assets, and seize new opportunities.


Integer Linear Programming in Computational and Systems Biology

By Dan Gusfield

Integer Programming and Computational Systems Biology” offers a transformative approach to biological computation. If you’re intrigued by the crossroads of biology and mathematical optimization, this book is a must-read. Here’s why:

  • In-Depth Examples: It offers real-world examples from various biological fields like genomics, phylogenetics, RNA, protein folding, and network analysis, among others.
  • Practical Workflow: The book aims to teach not just the logic of modeling and solving problems with ILP, but also the practical workflow involved in using ILP in biology.
  • Accessible to All: Written with a wide audience in mind, the book requires no biological or computational prerequisites, making it suitable for both entry-level courses and advanced studies.
  • Hands-On Learning: The book comes with numerous exercises and accompanying software in Python and Perl to help you grasp the practical aspects of using ILP in biology.


Introduction to Mathematical Optimization

By Matteo Fischetti

Introduction to Mathematical Optimization” by Matteo Fischetti serves as a comprehensive teaching aid for students delving into the realms of operations research and mathematical optimization. Here’s why you should consider adding it to your reading list:

  • Broad Coverage: The book covers essential topics like Linear Programming, Integer Linear Programming, Computational Complexity, and Graph Theory.
  • Focus on Integer Linear Programming: The book places particular emphasis on Integer Linear Programming, offering an in-depth exposition of the most recent resolution techniques, including the advanced branch-and-cut method.
  • Practical Learning: The book is enriched with numerous examples and exercises that make the learning process interactive and engaging.


Interesting Blogs

Nathan Brixius

Nathan Brixius’s blog is a treasure trove for anyone interested in mathematical optimization, machine learning, and the intersection of these fields with real-world applications. The blog covers a wide range of topics, from technical tutorials and code snippets to thought-provoking articles on the future of these disciplines.


Yet Another Math Programming Consultant

By Erwin Kalvelgen

Yet Another Math Programming Consultant” is a blog that serves as a rich repository of technical notes, insights, and solutions related to mathematical programming and optimization. Authored by Erwin Kalvelgen, a full-time consultant who specializes in the design, implementation, and deployment of mathematical programming and data-science applications, this blog is a goldmine for both practitioners and enthusiasts.


Punk Rock Operations Research

By Laura Albert

If you’re looking to delve into the world of operations research, the blog “Punk Rock Operations Research” by Laura Albert is a treasure trove of insights, discussions, and thought-provoking articles. The blog covers a wide range of topics, from the history and philosophy of operations research to its applications in sports analytics and engineering challenges. One of the standout pieces is a transcript of a lecture by Philip McCord Morse, which delves into the essence of operations research, emphasizing its flexibility, practicality, and data-driven nature. The blog also features conference recaps, discussions on academic research collaboration, and even a playful take on what to call a group of operations researchers.


The Optimization Edge Blog

By Princeton Consultants

The Optimization Edge Blog” by Princeton Consultants is a must-read for anyone interested in the practical applications of optimization and decision-making. Authored by experts in the field, the blog offers a unique blend of technical insights, industry trends, and real-world case studies. Topics range from the role of optimization in software development and design thinking to its impact on transportation, logistics, and supply chains. The blog also delves into the challenges faced by various industries, such as manufacturing and rail transportation, and how optimization can offer solutions.


OR in an OB World

By Paul A. Rubin

OR in an OB World” offers a candid look into the world of operations research and mathematical optimization. Paul Rubin’s approach is both practical and insightful, discussing real-world applications and challenges. Whether it’s a detailed explanation of file versioning in LyX, a typesetting system often used for academic papers, or tips on reducing drive clutter, the blog provides valuable insights that can benefit both newcomers and seasoned professionals. The blog also serves as a platform for sharing fixes and workarounds for common issues, making it a useful resource for anyone looking to navigate the complexities of operations research and mathematical optimization.


Mike Talks AI

By Michael Watson

Are you a business leader, data scientist, or simply an AI enthusiast looking to navigate the complex world of artificial intelligence? Look no further, because Mike Talks AI is the blog you need to follow.

Written by Mike Watson, this Substack publication offers a rich blend of content that ranges from practical AI applications in business to career advice for young data scientists. The blog is not just about theories; it’s about actionable insights that you can apply in your professional life. Whether you’re interested in operational excellence, network design, or the nuances of AI, Mike Talks AI has got you covered.

The blog delves into a variety of subjects that are crucial in today’s data-driven world. From discussing career moves that young data scientists often dismiss, to sharing lessons from Walmart’s innovative approach to network design, Mike Talks AI offers a balanced mix of thought leadership and practical advice.

So, if you’re ready to up your AI game and stay ahead of the curve, subscribing to Mike Talks AI is a decision you won’t regret.


Video Blogs and Social Media

Subject to (s.t.)

By Anand Subramanian

Subject to” offers a series of informal conversations with relevant figures in the fields of Operations Research, Combinatorial Optimization, and Logistics. Hosted by Anand Subramanian, an Associate Professor at Universidade Federal da Paraíba (UFPB) in Brazil, the channel serves as a platform for insightful dialogues that delve into the intricacies of these disciplines. Anand brings a rich background to the table, being an author of more than 55 articles published in prestigious international journals and boasting over 4,000 citations on Google Scholar. His channel is not just for academics; it’s for anyone who is passionate about these fields and wants to hear from the experts. Whether you’re a student, a professional, or simply someone interested in learning more about operations research and related areas, “Subject to” offers a unique and engaging way to deepen your understanding.


Know of some good books, blogs, and other resources we should check out and consider adding to our list? Send us an email at info@gurobi.com.

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