mersenneforum.org Convex Optimization - Stanford Online Course
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2014-01-08, 21:20   #1
wblipp

"William"
May 2003
New Haven

94116 Posts
Convex Optimization - Stanford Online Course

Is anyone else interested in taking this online course in Convex Optimization from Stanford University?

The Simplex method of solving Linear Programming problems gave way to Interior Point Methods, and that enabled generalization of the objective function to convex functions. Recent interest in the field had been driven by computing power enabling embedded real time applications and a wider grasp of the breadth of convex functions.

Even though free, this is a sophisticated class taught by the author of the leading text book on the subject. I know we have some people here with adequate background, but I don't know if there is also interest. I'll be taking the class.

Quote:
 Originally Posted by About CVX101 How hard is this class? This is an advanced class, targeting MS and PhD level students in mathematically sophisticated fields.

 2014-01-09, 22:30 #2 ewmayer ∂2ω=0     Sep 2002 República de California 23×1,459 Posts Are there any nontrivial applications to number theory? Several years ago, one of the bright-but-likes-to-hear-himself-opine-too-much regulars at my local SiVal coffee shop excitedly explained to me how LP could be applied to integer factorization, and the huge speedups which that promised. Alas, he had overlooked the crucial difference between LP over the reals and the integers - not dissimilar from the difference between factoring an integer over those disparate domains.
 2014-01-11, 17:02 #3 jasonp Tribal Bullet     Oct 2004 3×1,181 Posts I actually can't think of any applications of linear programming for number theory. It would be great if there were some, because it supposedly is easy to handle even very large size LP problems (say a million variables) and still get a global optimum. If there was a way to relate linear programming to lattice basis reduction, that would be huge and would have far-reaching implications for computational number theory. Last fiddled with by jasonp on 2014-01-11 at 17:04
2014-01-11, 22:14   #4
only_human

"Gang aft agley"
Sep 2002

EAA16 Posts

Quote:
 Originally Posted by jasonp If there was a way to relate linear programming to lattice basis reduction, that would be huge and would have far-reaching implications for computational number theory.
Thinking in that direction, although no one has mentioned it here, the release of Homotopy Type Theory with Univalent Foundations last year is a big deal and should lead to tools and approaches.

http://homotopytypetheory.org/book/

2014-01-12, 18:47   #5
CRGreathouse

Aug 2006

3·1,993 Posts

Quote:
 Originally Posted by only_human Thinking in that direction, although no one has mentioned it here, the release of Homotopy Type Theory with Univalent Foundations last year is a big deal and should lead to tools and approaches. http://homotopytypetheory.org/book/
I've heard this claim before. I'll be more receptive once I hear someone say, "I knew nothing of homotopy, I read the book, and now I've done something nontrivial with it in ___" where ___ is a field other than homotopy theory.

 2014-01-17, 16:44 #6 wblipp     "William" May 2003 New Haven 236910 Posts The Convex Optimization MOOC includes a 3 month license to MatLab. I installed last night without problems.

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