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This review is written from the perspective of a mathematically capable outsider to the field of Operations Research and Optimization that does research in statistics & machine learning. I have found that it's very difficult to figure out how to self-study these topics in general, so I'm going to include context & other resources I have found useful to highlight the importance and quality of this book. In my opinion, the landscape of OR and Optimization have to be understood to really appreciate it.
When I initially picked up Boyd & Vanderberghe, I got very frustrated with it. I would recommend going through introductory optimization material first (I went through "Managerial Decision Modeling with Spreadsheets" by Balakrishnan et al, which is excellent), and be comfortable with the basics of linear algebra and calculus, otherwise this book will seem more inaccessible than it actually is. I have also heard that Stephen Boyd's lectures on YouTube are an excellent supplement to the book and make the introduction far more gentle.
This book is a field manual for learning to recognize convex problems "in the wild": meaning, given an optimization problem, how do we make it easier to solve by making one or more parts of the problem convex? This process is known as "convex relaxation" and is one of the fundamental skills required for research in topics like statistics & machine learning, and probably many other fields as well. Because of this focus, the book strikes a very important middle ground between the highly applied side of case studies and model building, and the highly theoretical side of algorithms and convex analysis. It provides just enough theory to be able to work with problems, and just enough intuition on algorithms to know what's going on behind the scenes.
I don't know why, but most treatments I have seen of Optimization/Operations Research is presented with too much of a focus on either theory/algorithms, or case studies with barely any focus on the former. After reading this text and doing the exercises (for which the solutions are freely available online), the reader can expect to be able to formulate optimization problems, relax those problems to be more easily solvable, input the problems to an optimization solver like CVX (Matlab) or CVXPY (CVX, but in Python) and have an idea of what algorithms the solver will use to solve the problem.
From what I have seen so far, I believe this text alone is sufficient for a good initial background to do statistics & machine learning research. However, I don't believe it's enough for people who want to focus on the difficulties of Operations Research model building, writing optimization algorithms, or on theoretical topics like existence of solutions, convergence proofs for algorithms, etc.
For discussion on the challenges associated with building big optimization models, I recommend H. Paul Williams's "Model Building in Mathematical Programming" (2013)--multiple real-world problems, their model formulations, and solutions are presented, and it's just amazing practice for a budding analyst. I think the introductory chapters are definitely lacking though, and I recommend picking up "Managerial Decision Modeling with Spreadsheets", as I mentioned above.
For learning how to write numerical optimization algorithms, it is hard to go wrong with Nocedal's and Wright's "Numerical Optimization" (2006). The presentation is, like this book, crystal clear, but again requires the reader to have a good grasp on the basics of optimization, linear algebra, and calculus. The entire focus of the book is on algorithms to solve various optimization problems (not just convex problems!), but because of its age, it will not contain material on some of the newer algorithms that have found use. I would recommend looking through (free) online courses such as Ryan Tibshirani's "Machine Learning 10-725", Stephen Boyd's EE364A/EE364B sequence, and Emmanuel Candes's Math 301.
Unfortunately, I am not the right person to ask for book recommendations to learn the theory, but I have heard good things about books by Nesterov, Bertsekas, and Rockafellar. These are books that really demand the reader to have a background in mathematical analysis. From my limited searching, Bertsekas's books have solution manuals, have good geometric descriptions of the concepts, and are self-contained. The books "Convex Optimization Theory" (2009), "Convex Optimization Algorithms" (2015), and "Convex Analysis & Optimization" (2003) in particular might be a good place to start.
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Customers say
Customers find this book to be an excellent introduction to optimization, with fundamental concepts explained precisely. They appreciate its writing style, describing it as well-written and concise.
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30 customers mention content, 28 positive, 2 negative
This is the excellent book if you want to start learning about convex optimization in both fundamental background and the actual algorithm aspects.Read more
Great explanations and examples. Can skip the very technical sections and it still reads well....Read more
Very well written. Highly recommended for students and/or professionals working in optimization fieldRead more
Well written, extremely helpful.Read more
9 customers mention writing style, 9 positive, 0 negative
Very well written. Highly recommended for students and/or professionals working in optimization fieldRead more
Well written, extremely helpful.Read more
Quite simply, this is a wonderful text. Coupling this with Boyd's course at Stanford...Read more
...The writers tend to capture the theory of convex optimization in a concise way and further illustrate it by showing their applications....Read more
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Top reviews from other countries
- Aretha SpearsReviewed in the United Kingdom on June 16, 2025
Convex Optimization, Boyd and Vandenberghe
Format: HardcoverVerified Purchase - ImmoReviewed in Germany on February 16, 2020
rock solid intro to convex optimization
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YayaReviewed in France on April 23, 2013
Excellente introduction pour étudiant et professionnels en dehors du domaine.
Format: HardcoverVerified Purchase
