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Convex Optimization (2004) [pdf]

117 pointsby newsoulalmost 2 years ago

11 comments

smiley1437almost 2 years ago
I remember ago Lars Blackmore of SpaceX released a paper on soft landing Falcon 9, that&#x27;s the first time I&#x27;d encountered convex optimization<p><a href="https:&#x2F;&#x2F;www.semanticscholar.org&#x2F;paper&#x2F;Lossless-Convexification-of-Nonconvex-Control-Bound-A%C3%A7ikmese-Carson&#x2F;9209221aa6936426627bcd39b4ad0604940a51f9?p2df" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.semanticscholar.org&#x2F;paper&#x2F;Lossless-Convexificati...</a><p>It blew my mind that you could convexify non-convex curves into useful-for-optimization convex curves to optimize for so many things simultaneously (physics constraints, control thruster limitations, sensor constraints, g forces, etc) and it&#x27;s cool that part of the spectacular landings we get from SpaceX relies on it
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yellowcake0almost 2 years ago
One of my favorite math books, there&#x27;s also the companion text, <a href="https:&#x2F;&#x2F;web.mit.edu&#x2F;~jadbabai&#x2F;www&#x2F;EE605&#x2F;additional_exercises.pdf" rel="nofollow noreferrer">https:&#x2F;&#x2F;web.mit.edu&#x2F;~jadbabai&#x2F;www&#x2F;EE605&#x2F;additional_exercises...</a>, which contains a lot of interesting applications, presumably compiled by Boyd himself and his colleagues over the years.
mellingalmost 2 years ago
The videos for Boyd’s classes are on YouTube.<p>He’s also got an edX course you can audit for free.<p><a href="https:&#x2F;&#x2F;www.edx.org&#x2F;course&#x2F;convex-optimization?index=product&amp;queryID=9c2eb1365338c848c42b8c902f1bc587&amp;position=6&amp;linked_from=autocomplete&amp;c=autocomplete" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.edx.org&#x2F;course&#x2F;convex-optimization?index=product...</a>
vrcalmost 2 years ago
I 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.
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cpgxiiialmost 2 years ago
Convex optimization can be a really amazing tool. We use optimization extensively, both on actually convex problems, and on non-convex-but-practically-solvable problems in robotics.<p>The math surrounding optimization is great; however, the reality of optimization tools is still very poor. A competitive optimizer is a massive project, and outside of a number of mostly limited&#x2F;specialized solvers, the effective tools are all proprietary and very expensive (e.g. SNOPT, Gurobi, Mosek, CPLEX, etc). How solveable and stable your problems can be depends on these tools, and effective problem formulation (e.g. what and how many constraints you use, how you compute gradients) is essentially a black art learned through hard experience.<p>There&#x27;s a great example of the complexity difference between optimization and other tools in the world of motion planning for robots: we expect that any semi-competent undergrad can implement search- and sampling-based planners (e.g. A* or RRT), implementing a good optimizer for trajectory optimization is a multi-million dollar project.<p>The world of optimization desperately needs a MuJoCo-DeepMind moment, where a large interested company buys one of the major commercial optimization providers and makes their tools free and open source. This would really be transformative to the field.
Solvencyalmost 2 years ago
&quot;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...&quot;<p>Boy, and that&#x27;s just the opening paragraph of the introduction.<p>Exactly what arcane requisite elite math precursors are necessary to even remotely understand this?
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crabmusketalmost 2 years ago
Encountered this in my final year of University and audited half the online course before it went way beyond what I needed to know. Boyd was a great lecturer, and the content was fantastic. Really interesting stuff to know. I was applying it to model-predictive control, which is a super interesting set of algorithms as well.
mvcalderalmost 2 years ago
Professors 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.
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uptownfunkalmost 2 years ago
Does this have any application to SOTA ML?
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onosalmost 2 years ago
I’ve heard great things but it’s longer than I could commit to reading. Can anyone recommend a similar but more concise text?
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bltalmost 2 years ago
My grad school bible!