Working Through Boyd and Vandenberghe's Convex Optimization
The book is standard reading for anyone doing optimization work now. Boyd and Vandenberghe cover the material cleanly, but the exercises are where most people hit real problems. The solution manual exists in various forms around the internet, and figuring out which version to use and how to actually benefit from it is a bit of a process. I spent a semester working through this book with grad students who were coming from different backgrounds. Some had strong linear algebra, some had none. The exercises range from straightforward verification to genuinely tricky problems that require you to construct counterexamples or transform non-obvious problems into convex form. The manual helps, but not in the way people assume. The official solution manual covers most of the exercises. It's not exhaustive for every single problem, and the solutions tend to be concise to the point of being opaque if you haven't worked through the chapter carefully first. I found the most useful approach was to attempt the problem on my own, get stuck, then look at the manual only for the specific step I was blocked on. Reading the full solution after the fact is educational, but it doesn't replace the struggle of trying to solve it yourself.
One practical issue I ran into: the available PDFs online vary significantly in quality. Some have scanning errors, some skip chapters, and a few contain solutions with actual mistakes. I learned this the hard way when a student spent two days chasing an error in someone's posted solution that turned out to be wrong. The official Cambridge University Press version is the only one I trust fully, and even that has occasional typos in later editions. When in doubt, cross-reference with the errata page on Boyd's website. There's also a separate set of lecture notes and supplementary materials on Boyd's Stanford page that sometimes clarifies what the solution manual leaves ambiguous. I keep that bookmarked alongside the manual because the two complement each other better than either does alone. For people using this for a course, the main pitfall is relying on the manual too early. The learning happens in the struggle. If you're stuck on a duality gap problem or trying to reformulate a non-convex constraint, looking up the answer immediately robs you of understanding the transformation technique. Give yourself at least an hour per exercise before consulting the manual. The problems that matter most are the ones where you eventually figure it out without help.
Another thing nobody mentions: the notation in the solutions can feel dense because it assumes fluency. A solution might say "by strong duality" in two words when the jump requires checking Slater's condition explicitly. If you're new to this material, you'll need to fill in those gaps yourself by going back to the relevant theorem in the book. That's normal and expected. The book and its companion resources are worth the effort. The manual is a reference tool, not a shortcut. Use it that way and it serves you well.
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