Convex Optimization (2004) [pdf]
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Convex Optimization (2004) [pdf]
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Re: Convex Optimization (2004) [pdf]
#2I had the pleasure of taking this course with Prof. Boyd when he did a semester at MIT and it really was excellent. With a basic understanding of linear algebra and proofs it opened my eyes to so many techniques and ways to look at problems. It also lowered my fear of tackling more complex coursework because it motivated my interest. The only downside is that I became far too over reliant on the MATLAB package they made to pair with the course, so trying to implement some of the techniques later on from scratch took some doing.
Re: Convex Optimization (2004) [pdf]
#3I’ve heard great things but it’s longer than I could commit to reading. Can anyone recommend a similar but more concise text?
Re: Convex Optimization (2004) [pdf]
#4One of my favorite math books, there's also the companion text, https://web.mit.edu/~jadbabai/www/EE605/additional_exercises..., which contains a lot of interesting applications, presumably compiled by Boyd himself and his colleagues over the years.
Re: Convex Optimization (2004) [pdf]
#5"A mathematical optimization problem, or just optimization problem, has the form minimize f0(x) subject to fi(x) ≤ bi , i = 1, . . . , m. (1.1) Here the vector x = (x1, . . . , xn) is the optimization variable of the problem, the function f0 : R n → R is the objective function, the functions fi : R n → R, i = 1, . . . , m, are the (inequality) constraint functions, and the constants b1, . . . , bm are the limits, or bounds, for the constraints. A vector x ⋆ is called optimal, or a solution of the problem (1.1), if it has the smallest objective value among all vectors that satisfy the constraints: for any z with f1(z) ≤ b1, . . . , fm(z) ≤ bm, we have f0(z) ≥ f0(x ⋆ ). We generally consider families or classes of optimization problems, characterized by particular forms of the objective and constraint functions. As an important example, the optimization problem (1.1) is called a linear program if..."
Boy, and that's just the opening paragraph of the introduction.
Exactly what arcane requisite elite math precursors are necessary to even remotely understand this?
Re: Convex Optimization (2004) [pdf]
#6I’ve heard great things but it’s longer than I could commit to reading. Can anyone recommend a similar but more concise text?
Have you looked at the Python library and tutorial?
Re: Convex Optimization (2004) [pdf]
#7"A mathematical optimization problem, or just optimization problem, has the form minimize f0(x) subject to fi(x) ≤ bi , i = 1, . . . , m. (1.1) Here the vector x = (x1, . . . , xn) is the optimization variable of the problem, the function f0 : R n → R is the objective function, the functions fi : R n → R, i = 1, . . . , m, are the (inequality) constraint functions, and the constants b1, . . . , bm are the limits, or…
Once upon a time I mentioned in passing that I subscribed to the proceedings of SIGPLAN. My coworker shot his hand out to stop the conversation.
“You can read those??”
“A little more than half.”
I knew exactly what he meant, and was amused that “half” satisfied his sudden suspicion that I was an alien living among humans.
Re: Convex Optimization (2004) [pdf]
#8The videos for Boyd’s classes are on YouTube.
He’s also got an edX course you can audit for free.
https://www.edx.org/course/convex-optimization?index=product...
Re: Convex Optimization (2004) [pdf]
#9"A mathematical optimization problem, or just optimization problem, has the form minimize f0(x) subject to fi(x) ≤ bi , i = 1, . . . , m. (1.1) Here the vector x = (x1, . . . , xn) is the optimization variable of the problem, the function f0 : R n → R is the objective function, the functions fi : R n → R, i = 1, . . . , m, are the (inequality) constraint functions, and the constants b1, . . . , bm are the limits, or…
From the introduction: "The only background required of the reader is a good knowledge of advanced calculus and linear algebra. If the reader has seen basic mathematical analysis (e.g., norms, convergence, elementary topology), and basic probability theory, he or she should be able to follow every argument and discussion in the book."
It's a graduate-level course. If that paragraph is arcane, the book is probably a few courses in your future.
Re: Convex Optimization (2004) [pdf]
#10Professors Boyd and Vandenberghe really broke ground with this text. Prior to this, optimization algorithms and methods were very much locked up behind a metaphorical paywall: difficult to access literature with very high barriers to entry, and strictly commercial software offerings. They brought optimization to the masses and should be celebrated for it.