ConvexOptimizationIILecture11
Instructor (Stephen Boyd)
:Hey, I guess we’ll start. Let me just make a couple of
announcements. I guess we’ve combined the rewrite of the preliminary project proposal
with the midterm project review, and I think that’s due this Friday. Good, okay, it’s due
Friday. So that’s going to be that. Please you’re welcome to show me or the TAs if you
want a format scan. the TAs are now as nasty as I am, and they can scan something, just
walk down it and say, ‘That’s typesetting error. I’m not going to read any farther.’ Or
they’ll read down a halfpage and say, ‘What are the variables?’ and then throw it at you
with a sneer.
So I’ve trained them pretty well. The danger, of course, is then they start applying that to
the stuff I write, which has happened in the past. They say things like, ‘This isn’t
consistent. Use this phrase on this page and this one on the other one.’ And you look at
the two, and you say, ‘Yeah, that’s true, all right.’ The executive decision was made.
We’re going to switch around.
It’s not the natural order of the class, in fact, but it fits better with people who are doing
projects. So a bunch of people are doing projects that involve nonconvex problems, and
so today we switched around, and we’re going to do sequential convex programming
first, and then we’ll switch back to problems that are convex problems and things like
that. We’ll do largescale stuff next.
The good news is that we can actually pull this off, I think, in one day. So we’re going to
come back later. There’ll be several other lectures on problems that are not convex and
various methods. There’s going to be a problem on reluxations. We’re going to have a
whole study of L1 type methods for sparse solutions. Those will come later. But this is
really our first foray outside of convex optimization.
So it’s a very simple, basic method. There’s very, very little you can say about it
theoretically, but that’s fine. It’s something that works quite well. Don’t confuse it –
although it’s related to something called sequential quadratic programming. That’s
something you’ll hear about a lot if you go to Google and things like that. Those are
things that would come up. But I just wanted to collect together some of the topics that
come up.
Okay, so let’s do sequential convex programming. Let’s see here. There we go. Okay, so
I guess it’s sort of implicit for the entire last quarter and this one. I mean the whole point
of using convex optimization methods on convex problems is you always get the global
solution. I mean up to numerical accuracy. So marginal and numerical accuracy, you
always get the global solution, and it’s always fast. And that’s fast according to theorist.
If you want a complexity theory, there are bounds that grow like polynomials and various
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 Fall '09
 StephenBoyd
 Optimization, Mathematical optimization, Convex function, Convex Optimization, Convex analysis, trust region

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